File size: 104,640 Bytes
6fa4bc9 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 |
{
"paper_id": "2021",
"header": {
"generated_with": "S2ORC 1.0.0",
"date_generated": "2023-01-19T07:24:27.437204Z"
},
"title": "Applied Temporal Analysis: A Complete Run of the FraCaS Test Suite",
"authors": [
{
"first": "Jean-Philippe",
"middle": [],
"last": "Bernardy",
"suffix": "",
"affiliation": {
"laboratory": "Centre for Linguistic Theory and Studies in Probability",
"institution": "University of Gothenburg",
"location": {}
},
"email": ""
},
{
"first": "Stergios",
"middle": [],
"last": "Chatzikyriakidis",
"suffix": "",
"affiliation": {
"laboratory": "Centre for Linguistic Theory and Studies in Probability",
"institution": "University of Gothenburg",
"location": {}
},
"email": ""
}
],
"year": "",
"venue": null,
"identifiers": {},
"abstract": "In this paper, we propose an implementation of temporal semantics that translates syntax trees to logical formulas, suitable for consumption by the Coq proof assistant. The analysis supports a wide range of phenomena including: temporal references, temporal adverbs, aspectual classes and progressives. The new semantics are built on top of a previous system handling all sections of the FraCaS test suite except the temporal reference section, and we obtain an accuracy of 81 percent overall and 73 percent for the problems explicitly marked as related to temporal reference. To the best of our knowledge, this is the best performance of a logical system on the whole of the FraCaS.",
"pdf_parse": {
"paper_id": "2021",
"_pdf_hash": "",
"abstract": [
{
"text": "In this paper, we propose an implementation of temporal semantics that translates syntax trees to logical formulas, suitable for consumption by the Coq proof assistant. The analysis supports a wide range of phenomena including: temporal references, temporal adverbs, aspectual classes and progressives. The new semantics are built on top of a previous system handling all sections of the FraCaS test suite except the temporal reference section, and we obtain an accuracy of 81 percent overall and 73 percent for the problems explicitly marked as related to temporal reference. To the best of our knowledge, this is the best performance of a logical system on the whole of the FraCaS.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Abstract",
"sec_num": null
}
],
"body_text": [
{
"text": "The semantics of tense and aspect has been a long standing issue in the study of formal semantics since the early days of Montague Grammar and a number of different ideas have been put forth to deal with them throughout the years. Recent proposals include the works of the following authors: Dowty (2012); Prior and Hasle (2003) ; Steedman (2000) ; Higginbotham (2009) ; Fernando (2015) . The semantics of tense and aspect have been also considered in the study of Natural Language Inference (NLI). The various datasets for NLI that have been proposed by the years contain examples that have some implicit or explicit reliance on inferences related to tense and aspect. One of the early datasets used to test logical approaches, the FraCaS test suite (Cooper et al., 1996) contains a whole section dedicated to temporal and aspectual inference (section 7 of the dataset). This part of the FraCaS test suite has been difficult to tackle. That is, so far, no computational system has been capable to deal with it in its entirety: when authors report accuracy over the FraCaS test suite they skip this section. In fact, they also often skip the anaphora and ellipsis sections, the exception being the system presented by Chatzikyriakidis (2017, 2019) , which includes support for anaphora and ellipsis but still omit the temporal section. 1 In this paper, we take up the challenge of providing a computationally viable account of tense and aspect to deal with the section 7 of the FraCaS test suite. Our account is not meant to be a theoretically extensive account of tense and aspect, but rather an account that is driven by the need to cover the test suite in a way that is general enough to capture the test suite examples, while still covering the rest of the FraCaS test suite.",
"cite_spans": [
{
"start": 306,
"end": 328,
"text": "Prior and Hasle (2003)",
"ref_id": "BIBREF22"
},
{
"start": 331,
"end": 346,
"text": "Steedman (2000)",
"ref_id": "BIBREF24"
},
{
"start": 349,
"end": 368,
"text": "Higginbotham (2009)",
"ref_id": "BIBREF13"
},
{
"start": 371,
"end": 386,
"text": "Fernando (2015)",
"ref_id": "BIBREF12"
},
{
"start": 751,
"end": 772,
"text": "(Cooper et al., 1996)",
"ref_id": "BIBREF10"
},
{
"start": 1218,
"end": 1247,
"text": "Chatzikyriakidis (2017, 2019)",
"ref_id": null
},
{
"start": 1336,
"end": 1337,
"text": "1",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "The account is evaluated on the entailment properties of various temporal and aspectual examples, as given by the test suite. As such, we are not getting into the discussion of how tense and aspect might affect grammaticality or infelicitousness of various sentences. We assume that the sentences of the FraCaS suite are syntactically and semantically correct, and strive to produce accurate logical representations given that assumption. We further assume that the entailment annotations of various problems are valid, and we use those to evaluate the correctness of the logical representations of sentences.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "The paper is structured as follows: in Section 2, we give a brief summary of the computational frameworks whose various subsystems rely on. In particular, the Grammatical Framework is used to construct the syntactic parser, the Coq proof assistant checks all the reasoning and a monad-based dynamic semantics deals with Montague-style se- 1 One can consider that MacCartney and Manning (2007) have made a run against the whole test suite. However, they do not deal with multi-premise cases. Consequently only 36/75 cases in the temporal section are attempted. The general accuracy of the system is .59, and .61 for the temporal section. Our system, as shown Table 1 , presents considerable improvements in coverage and accuracy over that of MacCartney and Manning. mantics, and references (anaphora). We also provide some brief remarks on temporal semantics. In Section 3, we discuss the main aspects of the compositional semantics of our system, using various examples from the FraCaS suite to illustrate its effectiveness. In Section 5, we evaluate how our system performs with respect to the FraCaS suite. We ran the system across the whole suite: our system is thus the first which is capable of handling the complete FraCaS test suite. Yet, we are interested in particular in the performance on the temporal section. In Section 6, we conclude and discuss avenues for future work.",
"cite_spans": [
{
"start": 339,
"end": 340,
"text": "1",
"ref_id": null
},
{
"start": 363,
"end": 392,
"text": "MacCartney and Manning (2007)",
"ref_id": "BIBREF15"
},
{
"start": 741,
"end": 764,
"text": "MacCartney and Manning.",
"ref_id": null
}
],
"ref_spans": [
{
"start": 658,
"end": 665,
"text": "Table 1",
"ref_id": null
}
],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "Our temporal analysis places itself in the context of a complete NLI system -which is why we can test it on the FraCaS suite. In this section we give a brief overview of the phases of the system, referring the reader to published work for details.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "GF The first phase of the system, parsing, is taken care of by the Grammatical Framework (GF, Ranta (2004) ), which is a powerful parser generator for natural languages, based on type-theoretical abstract grammars. The present work leverages a syntactic representation of the FraCaS test suite in GF abstract syntax, in effect a GF FraCaS treebank (Ljungl\u00f6f and Siverbo, 2011) . Thanks to this, we skip the parsing phase and avoid any syntactic ambiguity. For the purpose of this paper, the important feature of GF syntax is that it aims at a balance of sufficient abstraction to provide a semanticallyrelevant structure, but at the same time it embeds sufficiently many syntactic features to be able to reconstruct natural-language text. That is, the parse trees generally satisfy the homomorphism requirement of Montague (1970 Montague ( , 1974 , and we can focus on the translation of syntactic trees to logical forms. Consequently, the system presented here does not aim at textual natural language understanding, but rather provides a testable, systematic formal semantics of temporal phenomena. Example (1) shows an example abstract syntax tree and its realisation in English.",
"cite_spans": [
{
"start": 94,
"end": 106,
"text": "Ranta (2004)",
"ref_id": "BIBREF23"
},
{
"start": 348,
"end": 376,
"text": "(Ljungl\u00f6f and Siverbo, 2011)",
"ref_id": "BIBREF14"
},
{
"start": 814,
"end": 828,
"text": "Montague (1970",
"ref_id": "BIBREF17"
},
{
"start": 829,
"end": 846,
"text": "Montague ( , 1974",
"ref_id": "BIBREF19"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "Dynamic Semantics Parse trees are then processed by a dynamic semantic component. Its role is essentially to support (non-temporal) anaphora, using a monadic-based dynamic semantics, gen-erally following the state of the art in this matter (Unger, 2011; Charlow, 2015 Charlow, , 2017 . Our particular implementation has weaknesses in certain areas (including group readings and counting; see Bernardy et al. (2020) for details) but non-temporal anaphoroi in the testsuite are generally resolved as they should be: on the whole accuracy is not affected significantly by issues in this subsystem.",
"cite_spans": [
{
"start": 240,
"end": 253,
"text": "(Unger, 2011;",
"ref_id": "BIBREF25"
},
{
"start": 254,
"end": 267,
"text": "Charlow, 2015",
"ref_id": "BIBREF7"
},
{
"start": 268,
"end": 283,
"text": "Charlow, , 2017",
"ref_id": "BIBREF8"
},
{
"start": 392,
"end": 414,
"text": "Bernardy et al. (2020)",
"ref_id": "BIBREF5"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "As it is the case for other basic phenomena, there is not much interaction between our treatment of time and non-temporal anaphora. Critical exceptions are discussed in Section 3 and Section 5.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "Montagovian Semantics Non-withstanding special support for anaphora, the core of the translation of syntax trees to logical form follows a standard montagovian semantics. In brief, sentences are interpreted as propositions, verbs and noun-phrases as predicates. We use type-raising of noun-phrases, to support quantifiers (Montague, 1974) .",
"cite_spans": [
{
"start": 322,
"end": 338,
"text": "(Montague, 1974)",
"ref_id": "BIBREF19"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "We support additionally the basic constructions and phenomena present in the testsuite, including adjectives, adverbs, nouns, verbs, anaphora, etc. The method is outlined by Montague (1970 Montague ( , 1973 ), but we direct the reader to our previous work for details Chatzikyriakidis (2017, 2019) , but the particular treatment of such phenomena is essentially independent from our treatment of time: in this paper we simply ignore these aspects beyond the fact that they are handled correctly in the FraCaS testsuite, except in a few pathological cases.",
"cite_spans": [
{
"start": 174,
"end": 188,
"text": "Montague (1970",
"ref_id": "BIBREF17"
},
{
"start": 189,
"end": 206,
"text": "Montague ( , 1973",
"ref_id": "BIBREF18"
},
{
"start": 268,
"end": 297,
"text": "Chatzikyriakidis (2017, 2019)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "Inference using Coq Logical forms are then fed to the Coq interactive theorem prover (proof assistant). Coq is based on the calculus of co-inductive constructions (Werner, 1994) We do not use any co-induction (or even induction) in this paper, relying on the pure lambda-calculus inner core of Coq. Coq is a very powerful reasoning engine that makes it fit for implementing natural language semantics. Coq also supports dependent typing and subtyping. Both concepts are instrumental in expressing NL semantics (Chatzikyriakidis and Luo, 2014) . Besides, on a more practical side, it works well for the the task of NLI, when the latter is formalised as a theorem proving task: its many tactics mean that many tasks in theorem proving are trivialised. In particular, all problems of time-intervals inclusion, which occur in every temporal problems, are solved with Coq's linear arithmetic tactic.",
"cite_spans": [
{
"start": 163,
"end": 177,
"text": "(Werner, 1994)",
"ref_id": "BIBREF27"
},
{
"start": 510,
"end": 542,
"text": "(Chatzikyriakidis and Luo, 2014)",
"ref_id": "BIBREF9"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Temporal-Semantics in a Logic-based NLI System",
"sec_num": "2"
},
{
"text": "In montagovian semantics, (intransitive) verbs are one-place predicates; in types, they are functions from entities to propositions (e \u2192 t). Our basic approach is to generalise the interpretation of verbs, so that it takes two additional time parameters, one corresponding to the starting time of the action and one corresponding to its stopping time ((e \u00d7 time \u00d7 time) \u2192 t). For example, if John walked between t 0 and t 1 , we would have: walk(john, t 0 , t 1 ). From now on we will call an interval of time points [t 0 , t 1 ] a timespan, where t 0 and t 1 are elements of the time type, which is represented in Coq as an abstract ordered ring. Every timespan [t 0 , t 1 ] has the property t 0 \u2264 t 1 : it starts no later than it stops. (We are thus using a simple Newtonian model of time, corresponding to a layman intuition of a linear constant flow of time.)",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "In principle, common nouns and adjectives should undergo the same procedure. For simplicity we will however only consider verbs from now on. (In fact, even in our implementation we chose not to extend nouns nor adjectives with timespan parameters. This choice limits the increase in complexity of the formulas compared to non-temporal semantics, at the expense of inaccuracy for a couple of problems in the FraCaS test suite: problems 271 and 272 use a an adjective as a copula which is subject to temporal reasoning.)",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(271) A unknown P1 Smith was present.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "P2 Jones was present.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "P3 Smith was present after Jones was present. H Jones was present before Smith was present.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Temporal Context We adjust the montagovian semantics so that the interpretation of every category (propositions, verb phrases, etc.) takes a temporal context as an additional parameter, which serves as a time reference for the interpretation of all time-dependent semantics within the phrase. (While some categories do not need this temporal context, we pass it everywhere for consistency.) This context propagates through the compositional interpretation down to lexical items with atomic representation (verbs). By default, every interpretation passes the temporal context down to its components without changing it. However some key elements will act on it on nontrivial ways, which we proceed to detail below. This temporal context is an optional timespan. That is, it can be a timespan or an explicitly unspecified context. The timespan in the context is optional because, in certain situations, the semantics is different depending on whether a timespan has been specified externally or not, as we explain below. A non-present timespan will be represented as \u2212. If a semantic function does not depend on the temporal context at all, we will write * instead.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Tenses The principal non-trivial manipulators of timespans are tense markers. In our syntax, inherited from GF, tenses are represented syntactically as an attribute of clauses. An illustration of a pasttense clause and its interpretation follows in Example (1). Notice in particular the past argument to the useCl constructor.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(1) A scandinavian won the nobel prize.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "useCl past pP os",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(predV P (detCN (detQuant indef Art numSg) scandinavian CN ) (complSlash (slashV \uf732a win V \uf732) (detCN (detQuant indef Art numSg) nobel prize CN )))",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "In our semantics we deal only with present and past tenses (simple and continuous). Indeed we find that FraCas does not exercise additional specific tenses. (When a more complicated tense is used, the additional information is also carried by adverbs or adverbial phrases, in a more specific way). While we believe that many other tenses can be captured under the same general framework, we leave a detailed study to further work. Even though we discuss a refinement to handle the past continuous at the end of this section, the procedure to handle tense annotations is as follows:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "\u2022 If the tense is the past, and the temporal context is unspecified, then we locally quantify over a time interval [t 0 , t 1 ], such that t 1 < now, where now is a logical constant representing the current timepoint. The temporal context then becomes this interval.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "\u2022 If the tense is the present and the temporal context is unspecified, then the temporal context becomes the simple (now, now) interval.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "\u2022 If the temporal context is specified (for example due to the presence of an adverb or an adverbial clause, such as \"before James swam\"), then the tense does not create a new interval, but it may constrain it. Typically, a past tense adds the constraint that the temporal context ends before the timepoint now.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Temporal Adverbs The other single most important source of interesting timespans are adverbs. Most of the temporal adverbs fall in either of the following categories:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "exact For such adverbs, an exact interval is provided. In fact, such adverbs typically specify a single point in time (so the start and the end of the interval coincide).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "at 5 pm, s ( * ) = s (5pm, 5pm)",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "existentially quantifying The majority of temporal adverbs existentially quantify over a timespan. Examples include \"since 1991\", \"in 1996\", \"for two years\", etc. The common theme is to introduce the interval and then restrict its bounds or its duration in some way. Sometimes the restriction is an equality, as in \"for exactly two hours\". In the following example we show the inclusion constraint, for \"in 1992\". in 1992,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "s ( * ) = \u2203t 1 , t 2 .[t 1 , t 2 ] \u2286 1992, s (t 1 , t 2 )",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "In the FraCaS test suite, we normally do not find several time-modifying adverbs modifying a single verb phrase. Indeed, sentences such as \"in 1992, in 1991 john wrote a novel\" are infelicitous. This justifies ignoring the input timespan in the above interpretation -we are in particular not interested in modelling felicity with our semantics, only giving an accurate semantics when the input is felicitous.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "universally quantifying A few adverbs introduce intervals via a universal quantification (sometimes with a constraint). Examples include \"always\" and \"never\".",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "If there is no explicit time context, then \"always\" has no constraint on the interval, otherwise the quantified interval must be included in it:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "always s (t 0 , t 1 ) = \u2200t 0 , t 1 .[t 0 , t 1 ] \u2286 [t 0 , t 1 ], s (t 0 , t 1 )",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Note that here we do use the input interval, resulting in a correct interpretation for phrases such as \"In 1994, Itel was always on time.\" .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Aside: aspectual classes in the literature In this paper we borrow several notions from classical temporal semantics such as \"stative\", \"achievement\", \"activity\", etc., even though our definitions do not perfectly match the classical ones. We explain our precise meaning for these terms in the body of the paper. Nevertheless, we refer the reader to Steedman (2000) for an extensive review of formal temporal semantics. For the cognoscenti, we can already point out some differences in terminology: we use the term activity as a general term which encompasses the three classical notions of activites, achievements and accomplishments. Indeed, insofar as the test suite is concerned, we find that these three categories can be collapsed into a single one (they are subject to Eq. (1)). That is, it is sufficient for the testsuite to distinguish between events and states. (In this paper, we always assume that the problems in the FraCaS testsuite are correctly annotated.)",
"cite_spans": [
{
"start": 350,
"end": 365,
"text": "Steedman (2000)",
"ref_id": "BIBREF24"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Time references and aspectual classes A common theme in the testsuite is the reference to previous occurrences of an event: To be able to conclude that there is entailment, as the testsuite expects, we have to make sure that the two occurrences of \"Jones left\" (in P1 and P2) refer to the same time intervals. For this purpose we postulate unicity of action for certain time-dependent propositions:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "unicity P : P (t 1 , t 2 ) \u2192 P (t 3 , t 4 ) \u2192 (t 1 = t 3 ) \u2227 (t 2 = t 4 ) (1)",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Unicity of action holds only if the aspectual class of the proposition P is activity (Steedman, 2000) (which, for our purposes, includes achievements and accomplishments as well).",
"cite_spans": [
{
"start": 85,
"end": 101,
"text": "(Steedman, 2000)",
"ref_id": "BIBREF24"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(The difference between activity and accomplishments on the one hand and achievement on the other hand is that for the latter, time intervals can be assumed to be of nil duration. In reality, this is an oversimplification as achievements are usually of short duration, but not nil. However, this plays little role in our analysis. As far as we can tell the FraCaS test suite does exercise temporal semantics to such a level of precision.)",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Unicity of action plays the role of event coreference in (neo-)Davidsonian accounts (Parsons, 1990) . It is also a fine-grained principle, allowing coreference to take into account certain arguments when referencing. As we detail below, taking arguments into account yields is critical to handle repeatability of achievements.",
"cite_spans": [
{
"start": 84,
"end": 99,
"text": "(Parsons, 1990)",
"ref_id": "BIBREF21"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Unicity of action appears to be a non-logical principle. Indeed, it is quite possible that \"Jones left\" several times. However, it seems that this principle is never contradicted by the testsuite. As such, even though unicity of action is only a pragmatic rule, it can be taken as a valid one by default: it is only when we have a sufficiently constrained situation that one should reject it. Consider the following discourse:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(1) Smith left at 1pm.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(2) Smith went to his appointment with the lawyer. (3) Smith left at 4pm.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "One would normally not say that there is contradiction. However if the middle sentence were not present, a contradiction should be flagged. We leave such discourse analysis as future work, and simply apply unicity of action everywhere: it is valid uniformly in the FraCaS test suite for activity aspect classes.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Statives A contrario, if P is stative, then we get a time-interval subsumption property:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "subsumption P : [t 3 , t 4 ] \u2286 [t 1 , t 2 ] \u2192 P (t 1 , t 2 ) \u2192 P (t 3 , t 4 )",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "This principle is used to reason about problem (314), below (note that \"Smith\" is used as a surname in the FraCaS and can take both feminine and masculine values):",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(314) P1 Smith arrived in Paris on the 5th of May, 1995. P2 Today is the 15th of May, 1995. P3 She is still in Paris. H Smith was in Paris on the 7th of May, 1995.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Indeed, from P3 we get that Smith was in Paris between May 5th and May 15th. Because \"being in Paris\" is stative, we also get that Smith was in Paris in any sub-interval. Contrary to unicity of action, subsumption is always valid.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Class-modifying adverbs It should be noted that some adverbs can locally disable the application of subsumption. For example, problem 299 features the sentence \"Smith lived in Birmingham for exactly a year\". Even though \"live\" is normally stative, one can no longer apply subsumption in the context of \"exactly a year\" -this can be done by propagating another context flag in the montagovian semantics (in addition to the temporal context).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(Un)repeatable Achievements The principle of using unicity of action interacts well with the usual interpretation of existential quantifiers (and anaphora). Indeed, using it, we can refute problem (279), as expected by the testsuite:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(279) P1 Smith wrote a novel in 1991.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "H Smith wrote it in 1992.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Indeed, following our account, the above (contradictory) inference problem is to be interpreted as",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "\u2200x.novel(x)\u2227 \u2203t 1 , t 2 .[t 1 , t 2 ] \u2286 1991 \u2227 write(smith, x, t 1 , t 2 )\u2227 \u2203t 3 , t 4 .[t 3 , t 4 ] \u2286 1992 \u2227 write(smith, x, t 3 , t 4 ) \u2212\u2192\u22a5",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(2) Note here that the scope for the existential is extended beyond the scope of P1, and its polarity switched (to universal). This extension can follow the account of Unger (2011), and our implemented analysis of anaphora (Bernardy et al., 2020; Bernardy and Chatzikyriakidis, 2019) .",
"cite_spans": [
{
"start": 223,
"end": 246,
"text": "(Bernardy et al., 2020;",
"ref_id": "BIBREF5"
},
{
"start": 247,
"end": 283,
"text": "Bernardy and Chatzikyriakidis, 2019)",
"ref_id": "BIBREF4"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Thanks to the unicity of action of write(smith, x, ...) (the subject and direct object are fixed) we find [t 1 , t 2 ] = [t 3 , t 4 ], and due to the years 1991 and 1992 being disjoint we obtain contradiction. In sum, no special notion of accomplishment is needs to be invoked: we only need the principle of unicity of action.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Yet, the testsuite instructs that we should not be able to refute problem (280), with the justification that \"wrote a novel\" is a repeatable accomplishment:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(280) P1 Smith wrote a novel in 1991.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "H Smith wrote a novel in 1992.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Here our interpretation is:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "(\u2203x.novel(x)\u2227 \u2203t 1 , t 2 .[t 1 , t 2 ] \u2286 1991 \u2227 write(smith, x, t 1 , t 2 ))\u2227 (\u2203y.novel(y)\u2227 \u2203t 3 , t 4 .[t 3 , t 4 ] \u2286 1992 \u2227 write(smith, y, t 3 , t 4 )) \u2212\u2192\u22a5",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Our analysis does not need to treat this last case specially. Indeed, even if write(smith, x, ., .) is an activity and thus subject to unicity of action, in (280), x is quantified existentially; we have two different actions: write(smith, x, t 1 , t 2 ) and write(smith, y, t 3 , t 4 ), because x = y, and thus we cannot deduce equality of the intervals t 1 , t 2 and t 3 , t 4 . In turn, the hypothesis cannot be refuted.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Action-modification Verbs The final class of lexemes carrying a temporal-dependent semantics are verbs taking a proposition as argument, like \"finish\", \"start\", etc. These verbs modify the temporal context in non-trivial ways. Consider for example \"finish to ...\". The timespan of the argument of \"finish\" should end within the timespan of the finishing action:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "finish to s (t 0 , t 1 ) = \u2203(t 0 , t 1 ).t 1 \u2208 [t 0 , t 1 ] \u2227 s (t 0 , t 1 )",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Progressive Aspect We treat verbs in the progressive form as different semantically from the non-progressive form. For example, \"John was writing a book\" is encoded as \u2203(t 1 , t 2 ).t 1 \u2264 t 2 , t 2 \u2264 now, P ROG write(John, book, t 1 , t 2 ), while \"John wrote a book\" is encoded as \u2203(t 1 , t 2 ).t 1 \u2264 t 2 , t 2 \u2264 now, write(John, book, t 1 , t 2 ). This distinction is necessary because in our analysis the progressive form (P ROG write) is subject to subsumption. That is, if John is writing in the interval [t 1 , t 2 ] then he is writing in any sub-interval of [t 1 , t 2 ]. This interpretation corresponds to the idea that the action takes place continuously over the whole interval. However, the same cannot be said of the non-continuous form (write): the end-points of the interval indicate the time needed to complete the achievement. (For example, \"John wrote a book in 1993\" neither entails \"John wrote a book in January 1993\" nor \"John wrote a book in December 1993\".) (In fact, write, in the non-progressive from, is on the contrary subject to unicity.) Finally, we also have write(x, y, t 1 , t 2 ) \u2192 P ROG write(x, y, t 1 , t 2 ).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "That is, the achievement (or activity in our terminology) variant implies the stative variant, for the same interval. Consequently we get the entailment from \"John wrote a book in 1993\" to \"John was writing a book in 1993\", but not the other way around.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "We note however that this interpretation differs only slightly from the usual accounts of the progressive in the literature. Ogihara (2007) summarises the position of Bennett and Partee (1978) as follows: a progressive sentence is true at an inter-",
"cite_spans": [
{
"start": 125,
"end": 139,
"text": "Ogihara (2007)",
"ref_id": "BIBREF20"
},
{
"start": 167,
"end": 192,
"text": "Bennett and Partee (1978)",
"ref_id": "BIBREF2"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "val [t 0 , t 1 ] iff there is an interval [t 0 , t 1 ] such that [t 0 , t 1 ]",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "is a non-final subinterval of [t 0 , t 1 ] and the progressive sentence is true at [t 0 , t 1 ]. This is very similar to our approach (subsumption for the progressive form only), but there is a difference regarding final intervals. Yet in our view this difference is hard to justify: we cannot see why \"John was writing a book in 1993\" entails that he was writing it January, February, etc. but not in December. Ogihara (2007) argues that this simple account of the progressive fails to reject a sentence such as \"Lee is resembling Terri.\" while \"Lee is walking\" is acceptable. We argue instead that the latter should be rejected for pragmatic reasons. Indeed, when a predicate holds for a very long interval, one typically uses the simple present tense in English. Therefore the continuous form pragmatically implies that the predicate holds for a limited interval. But, without further context, the predicate \"resemble Terri\" does not vary over time (while \"walk\" generally does). Therefore the continuous form \"Lee is resembling Terri\" is confusing: one implies a limited interval, but the semantics of resembling normally yield an unlimited interval. Because we do not account for pragmatics, we prefer to retain the simplest account based on the subinterval property (which we call subsumption here).",
"cite_spans": [
{
"start": 412,
"end": 426,
"text": "Ogihara (2007)",
"ref_id": "BIBREF20"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "Finally we stress that not all verbs are subject to the stative/achievement distinction induced by the progressive. For example, the phrases \"John ran\" and \"John was running\" appear to be logically equivalent, for entailment purposes.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Our Treatment of Time",
"sec_num": "3"
},
{
"text": "To give a sense of the additional details necessary to deal with the precision demanded by a proofassistant such as Coq we show how problem (279) is worked out in full details.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "We start with input trees in GF format, given by Ljungl\u00f6f and Siverbo (2011) . They can be rendered as follows: s_279_1_p= sentence (useCl past pPos (predVP (usePN (lexemePN \"smith_PN\")) (advVP (complSlash (slashV2a (lexemeV2 \"write_V2\"))) (detCN (detQuant indefArt numSg) (useN (lexemeN \"novel_N\")))) (lexemeAdv \"in_1991_Adv\"))) s_279_3_h= sentence (useCl past pPos (predVP (usePN (lexemePN \"smith_PN\")) (advVP (complSlash (slashV2a (lexemeV2 \"write_V2\")) (usePron it_Pron)) (lexemeAdv \"in_1992_Adv\"))))",
"cite_spans": [
{
"start": 49,
"end": 76,
"text": "Ljungl\u00f6f and Siverbo (2011)",
"ref_id": "BIBREF14"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "Of particular note is the use of the pronoun \"it\", and the fact that adverbial expressions such that \"in 1992\" are lexicalized. We also follow the GF convention to postfix lexical items with the name of their category. Most of the other categories follow usual naming conventions. We remind the reader that \"slash\" categories are used to swap the order of arguments (compared to non-slashed categories of similar names).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "Our dynamic and temporal semantics gives the following interpretation for s_279_1_p implies s_279_3_h. (IS_INTERVAL Date_19920101 f /\\ IS_INTERVAL g Date_19921231 /\\ IS_INTERVAL f g /\\ appTime f g (write_V2 a) (PN2object smith_PN)))))).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "In the above, one should remark the top-level quantification over the novel (as explained in Section 3), the quantification over time intervals as individual timepoints, and the use of custom operators for several constructions (FORALL, Not, IS_INTERVAL, appTime). This use of custom operators is useful for several generalisations (for example, we have quantifiers such as MOST in addition to FORALL -see Bernardy and Chatzikyriakidis (2017) ) Unfolding the definitions for these operators yield the following proposition:",
"cite_spans": [
{
"start": 406,
"end": 444,
"text": "Bernardy and Chatzikyriakidis (2017) )",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "forall x : object, novel_N x -> (exists b c : Z, Date_19910101 <= b /\\ c <= Date_19911231 /\\ b <= c /\\ write_V2 x SMITH b c) -> (exists f g : Z, Date_19920101 <= f /\\ g <= Date_19921231 /\\ f <= g /\\ write_V2 x SMITH f g) -> False",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "This is very close to our idealised representation of the problem Eq. (2). One difference is the use of abstract Coq integers for timepoints. Using a discrete time allows us to use predefined Coq tactics. The discrete nature of integers does not interfere with the reasoning.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "Finally, we can show a Coq proof for the above proposition: The intros and destruct tactics serve bookkeeping purposes. The critical part is the use of the writeUnique axiom, which witnesses the aspectual class of the predicate write V2. The proof is completed by the use of the lia tactic, which is embeds a decision procedure for linear arithmetic problems 2 . Fortunately, lia can take care of all the problems which arise in the FraCaS testsuite.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Worked out example",
"sec_num": "4"
},
{
"text": "Our target is the FraCaS testsuite, which aims at covering a wide range of common natural-language phenomena. The suite is structured according to the semantic phenomena involved in the inference process for each example, and contains nine sections: Quantifiers, Plurals, Anaphora, Ellipsis, Adjectives, Comparatives, Temporal, Verbs and Attitudes. The system described here focuses on the Temporal section. However, it also supports the other eight sections. To our knowledge this is the first system which attempts to target the temporal section in full. But in fact, our system even provides support for all the other sections. Thus, a couple of decades Table 1 : Accuracy of our system compared to others. \"This\" refers to the approach presented in this paper. When a system does not handle the nominal number of test cases (shown in the second column), the actual number of test cases attempted is shown below the accuracy figure, in smaller font. \"FC\" refers to the work of Bernardy and Chatzikyriakidis (2017) , and \"FC2\" its followup (Bernardy and Chatzikyriakidis, 2019) . \"MINE\" refers to the approach of Mineshima et al. (2015) , \"NUT\" to the CCG system that utilises the first-order automated theorem prover nutcracker (Bos, 2008) , and \"LP\" to the system presented by Abzianidze (2015). A dash indicates that no attempt was made for the section.",
"cite_spans": [
{
"start": 980,
"end": 1016,
"text": "Bernardy and Chatzikyriakidis (2017)",
"ref_id": "BIBREF3"
},
{
"start": 1042,
"end": 1079,
"text": "(Bernardy and Chatzikyriakidis, 2019)",
"ref_id": "BIBREF4"
},
{
"start": 1115,
"end": 1138,
"text": "Mineshima et al. (2015)",
"ref_id": "BIBREF16"
},
{
"start": 1231,
"end": 1242,
"text": "(Bos, 2008)",
"ref_id": "BIBREF6"
}
],
"ref_spans": [
{
"start": 657,
"end": 664,
"text": "Table 1",
"ref_id": null
}
],
"eq_spans": [],
"section": "Results and Evaluation",
"sec_num": "5"
},
{
"text": "after its formulation, we propose a first attempt at covering the whole suite. As such, there it is no other system to compare our system with, in all aspects. We can however compare with systems which target parts of the FraCaS testsuite, as shown in Table 1 .",
"cite_spans": [],
"ref_spans": [
{
"start": 252,
"end": 259,
"text": "Table 1",
"ref_id": null
}
],
"eq_spans": [],
"section": "Results and Evaluation",
"sec_num": "5"
},
{
"text": "Interaction with anaphora One reason explaining the lower performance of our system on some sections of the testsuite is that our interpretation of time interacts imperfectly with anaphora and ellipsis. Consider the following example:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Results and Evaluation",
"sec_num": "5"
},
{
"text": "(232) P1 ITEL won more orders than APCOM did. P2 APCOM won ten orders. H ITEL won at least eleven orders.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Results and Evaluation",
"sec_num": "5"
},
{
"text": "In the first premise, our system essentially resolves the ellipsis to get the following reading: \"ITEL won X orders and APCOM won Y orders and X > Y .\". One would need each of the verb phrases \"won X orders\" and \"won Y orders\" to introduce their own timespans with existential quantifiers. However, the organisation of our system is such that the existentials are introduced before the ellipsis is expanded. Consequently we get a wrong interpretation and the inference cannot be made.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Results and Evaluation",
"sec_num": "5"
},
{
"text": "We have presented a first attempt for a computational approach dealing with the temporal section of the FraCaS test suite. To do this, we have provided a simplified taxonomy of aspectual classes for verb phrases, guided by the applicability of the unicity of action and temporal subsumption properties. While part of this simplification is accidental (conflation of activity and accomplishment), we find that other parts (the automatic distinction between repeatable and unrepeatable achievements) constitute theoretical improvements.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "Besides inference, formal interpretation of tense is found in natural-language interfaces to databases. Of note is the work of Androutsopoulos et al. (1998) , which handles many of the time-aware adverbial clauses that we address. However, we cover many more logical aspects of inference, such as coreference via unity of action and interaction with quantifiers.",
"cite_spans": [
{
"start": 127,
"end": 156,
"text": "Androutsopoulos et al. (1998)",
"ref_id": "BIBREF1"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "Bernardy and Chatzikyriakidis (2019) presented a logical system for handling 8 of the 9 sections of the FraCaS test suite, but excluded section 7, suggesting that it requires many examples that need an ad hoc treatment. Here, we took up this challenge and have shown that a system similar to theirs can be extended to cover the remaining section of the test suite, without considerably decreasing the performance of the rest of the sections. This is indeed a common problem with logical approaches, namely the fact that one can have theoretically motivated implementations of individual phenomena, e.g. anaphora, ellipsis, quantifiers, temporal reference etc., but when one tries to put all these together into a unified system, this proves to be a daunting task. We believe that this paper presents an exception, and provides a system that can deal with all these different semantic phenomena under a unified system with very good results. We use the same combination of a number of well-studied tools as Bernardy and Chatzikyriakidis (2019) : type theory, parsing using the Grammatical Framework (GF), Monadic Dynamic Semantics and proof assistant technology (Coq). The system achieves an accuracy of 0.73 on the Temporal Section and 0.81 overall. The whole system, including data sets, is available at the following url: https://github. com/GU-CLASP/FraCoq/tree/iwcs2021.",
"cite_spans": [
{
"start": 1006,
"end": 1042,
"text": "Bernardy and Chatzikyriakidis (2019)",
"ref_id": "BIBREF4"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "One of the things to be looked at is fixing the issues associated with parts of the test suite that \"broke\" when the temporal analysis was introduced. Some of these have been already mentioned: interaction of the temporal variables with anaphora.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "Another extension of this work is to reflect more temporal semantic inference properties in an extended test suite. Indeed, there as properties which are not captured in the FraCaS test suite, such as fine-grained examples of lexical and grammatical aspect, as well as the interaction between those two, for example cases where one needs to actually distinguish between achievements and accomplishments on the basis of their inferential properties:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "( * 1) P1 John found his keys.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "H John was finding his keys (UNK).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "( * 2) P1 John wrote a book. H John was writing a book (YES).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "In the first of the two examples involving an achievement verb, the inference is UNK, since there is no guarantee that the action is noninstantaneous. To the contrary, for accomplishment verbs, the inference follows.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "Further cases to be included in an extended Fra-CaS future suite involve examples where the interaction between different tenses needs to be captured: 3 ( * 3) P1 When the phone rang, John had entered the house. H John entered the house before the phone rang (YES).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "Finally it would be desirable to improve automation of the system, and evaluate it on a larger test set. As it stands Coq fully checks the proof of entailment for each (provable) problem. However, the construction of such proofs has demanded human intervention. It would be desirable to fully automate the proof construction step. For this to make sense however we need a much larger test suite, properly separated into a development and a (secret) test set. Otherwise, only the limited power 3 While this work was completed, the work by (Vashishtha et al., 2020) was published. The authors present a five datasets to be used for the training of neural models' ability to capture temporal reasoning. It would be interesting to check the amount of data covered, most specifiaclly the level of finegrainedness of temporal reasoning needed to capture those examples, as compared to what we have been discussing in this paper. We thank an anonymous reviewer for bringing this work to our attention. of the logic prevents us (or any followup work) to fine-tune the rules of the system until one gets full coverage. This kind of observation holds in general of any rule-based system, and thus applies not only to the proof-construction phase, but also to the underlying dynamic semantics and parsing phase (which is limited only by the power of the language and frameworks used for its implementation). In sum, contrary to statistical approaches to language understanding, the value of the present work lies not in the bare accuracy numbers which we are able to achieve, but in the details of how we do so: the of set of rules which we use, which is described in detail here and in the work which we base ourselves upon (Bernardy et al., 2020; Bernardy and Chatzikyriakidis, 2019) .",
"cite_spans": [
{
"start": 538,
"end": 563,
"text": "(Vashishtha et al., 2020)",
"ref_id": "BIBREF26"
},
{
"start": 1714,
"end": 1737,
"text": "(Bernardy et al., 2020;",
"ref_id": "BIBREF5"
},
{
"start": 1738,
"end": 1774,
"text": "Bernardy and Chatzikyriakidis, 2019)",
"ref_id": "BIBREF4"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusions and Future Work",
"sec_num": "6"
},
{
"text": "It solves linear goals over rings by searching for linear refutations and cutting planes",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
}
],
"back_matter": [
{
"text": "The research reported in this paper was supported by grant 2014-39 from the Swedish Research Council, which funds the Centre for Linguistic Theory and Studies in Probability (CLASP) in the Department of Philosophy, Linguistics, and Theory of Science at the University of Gothenburg. We are grateful to our colleagues in CLASP for helpful discussion of some of the ideas presented here. We also thank anonymous reviewers for their useful comments on an earlier draft of the paper.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Acknowledgements",
"sec_num": null
}
],
"bib_entries": {
"BIBREF0": {
"ref_id": "b0",
"title": "A tableau prover for natural logic and language",
"authors": [
{
"first": "",
"middle": [],
"last": "Lasha Abzianidze",
"suffix": ""
}
],
"year": 2015,
"venue": "Proceedings of EMNLP15",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Lasha Abzianidze. 2015. A tableau prover for natural logic and language. In Proceedings of EMNLP15.",
"links": null
},
"BIBREF1": {
"ref_id": "b1",
"title": "Time, tense and aspect in natural language database interfaces",
"authors": [
{
"first": "Ion",
"middle": [],
"last": "Androutsopoulos",
"suffix": ""
},
{
"first": "Graeme",
"middle": [
"D"
],
"last": "Ritchie",
"suffix": ""
},
{
"first": "Peter",
"middle": [],
"last": "Thanisch",
"suffix": ""
}
],
"year": 1998,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Ion Androutsopoulos, Graeme D Ritchie, and Peter Thanisch. 1998. Time, tense and aspect in natural language database interfaces. arXiv preprint cmp- lg/9803002.",
"links": null
},
"BIBREF2": {
"ref_id": "b2",
"title": "Toward the logic of tense and aspect in English",
"authors": [
{
"first": "Michael",
"middle": [],
"last": "Bennett",
"suffix": ""
},
{
"first": "Barbara",
"middle": [
"Hall"
],
"last": "Partee",
"suffix": ""
}
],
"year": 1978,
"venue": "",
"volume": "84",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Michael Bennett and Barbara Hall Partee. 1978. To- ward the logic of tense and aspect in English, vol- ume 84. Indiana University Linguistics Club Bloom- ington.",
"links": null
},
"BIBREF3": {
"ref_id": "b3",
"title": "A type-theoretical system for the fracas test suite: Grammatical framework meets coq",
"authors": [
{
"first": "Jean-",
"middle": [],
"last": "",
"suffix": ""
},
{
"first": "Philippe",
"middle": [],
"last": "Bernardy",
"suffix": ""
},
{
"first": "Stergios",
"middle": [],
"last": "Chatzikyriakidis",
"suffix": ""
}
],
"year": 2017,
"venue": "IWCS 2017-12th International Conference on Computational Semantics-Long papers",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Jean-Philippe Bernardy and Stergios Chatzikyriakidis. 2017. A type-theoretical system for the fracas test suite: Grammatical framework meets coq. In IWCS 2017-12th International Conference on Computa- tional Semantics-Long papers.",
"links": null
},
"BIBREF4": {
"ref_id": "b4",
"title": "A wide-coverage symbolic natural language inference system",
"authors": [
{
"first": "Jean-",
"middle": [],
"last": "",
"suffix": ""
},
{
"first": "Philippe",
"middle": [],
"last": "Bernardy",
"suffix": ""
},
{
"first": "Stergios",
"middle": [],
"last": "Chatzikyriakidis",
"suffix": ""
}
],
"year": 2019,
"venue": "Proceedings of the 22nd Nordic Conference on Computational Linguistics. ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Jean-Philippe Bernardy and Stergios Chatzikyriakidis. 2019. A wide-coverage symbolic natural language inference system. In Proceedings of the 22nd Nordic Conference on Computational Linguistics. ACL.",
"links": null
},
"BIBREF5": {
"ref_id": "b5",
"title": "A computational treatment of anaphora and its algorithmic implementation: Extended version",
"authors": [
{
"first": "Jean-Philippe",
"middle": [],
"last": "Bernardy",
"suffix": ""
},
{
"first": "Stergios",
"middle": [],
"last": "Chatzikyriakidis",
"suffix": ""
},
{
"first": "Aleksandre",
"middle": [],
"last": "Maskharashvili",
"suffix": ""
}
],
"year": 2020,
"venue": "Available on the first author's homepage",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Jean-Philippe Bernardy, Stergios Chatzikyriakidis, and Aleksandre Maskharashvili. 2020. A computational treatment of anaphora and its algorithmic implemen- tation: Extended version. Available on the first author's homepage: https://jyp.github.io/ pdf/phoroi.pdf or online https://bit.ly/ 2xQ4G2M.",
"links": null
},
"BIBREF6": {
"ref_id": "b6",
"title": "Wide-coverage semantic analysis with boxer",
"authors": [
{
"first": "Johan",
"middle": [],
"last": "Bos",
"suffix": ""
}
],
"year": 2008,
"venue": "Step 2008 conference proceedings",
"volume": "",
"issue": "",
"pages": "277--286",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Johan Bos. 2008. Wide-coverage semantic analysis with boxer. In Semantics in text processing. Step 2008 conference proceedings, pages 277-286.",
"links": null
},
"BIBREF7": {
"ref_id": "b7",
"title": "Monadic dynamic semantics for anaphora. Ohio State Dynamic Semantics Workshop",
"authors": [
{
"first": "Simon",
"middle": [],
"last": "Charlow",
"suffix": ""
}
],
"year": 2015,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Simon Charlow. 2015. Monadic dynamic semantics for anaphora. Ohio State Dynamic Semantics Work- shop.",
"links": null
},
"BIBREF8": {
"ref_id": "b8",
"title": "A modular theory of pronouns and binding",
"authors": [
{
"first": "Simon",
"middle": [],
"last": "Charlow",
"suffix": ""
}
],
"year": 2017,
"venue": "Logic and Engineering of Natural Language Semantics (LENLS)",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Simon Charlow. 2017. A modular theory of pronouns and binding. In Logic and Engineering of Natural Language Semantics (LENLS) 14. Springer.",
"links": null
},
"BIBREF9": {
"ref_id": "b9",
"title": "Natural language inference in coq",
"authors": [
{
"first": "Stergios",
"middle": [],
"last": "Chatzikyriakidis",
"suffix": ""
},
{
"first": "Zhaohui",
"middle": [],
"last": "Luo",
"suffix": ""
}
],
"year": 2014,
"venue": "Journal of Logic, Language and Information",
"volume": "23",
"issue": "4",
"pages": "441--480",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Stergios Chatzikyriakidis and Zhaohui Luo. 2014. Nat- ural language inference in coq. Journal of Logic, Language and Information, 23(4):441-480.",
"links": null
},
"BIBREF10": {
"ref_id": "b10",
"title": "Using the framework",
"authors": [
{
"first": "R",
"middle": [],
"last": "Cooper",
"suffix": ""
},
{
"first": "D",
"middle": [],
"last": "Crouch",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Van Eijck",
"suffix": ""
},
{
"first": "C",
"middle": [],
"last": "Fox",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Van Genabith",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Jaspars",
"suffix": ""
},
{
"first": "H",
"middle": [],
"last": "Kamp",
"suffix": ""
},
{
"first": "D",
"middle": [],
"last": "Milward",
"suffix": ""
},
{
"first": "M",
"middle": [],
"last": "Pinkal",
"suffix": ""
},
{
"first": "M",
"middle": [],
"last": "Poesio",
"suffix": ""
},
{
"first": "S",
"middle": [],
"last": "Pulman",
"suffix": ""
}
],
"year": 1996,
"venue": "The FraCaS consortium",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "R. Cooper, D. Crouch, J. van Eijck, C. Fox, J. van Gen- abith, J. Jaspars, H. Kamp, D. Milward, M. Pinkal, M. Poesio, and S. Pulman. 1996. Using the framework. Technical report LRE 62-051r, The FraCaS consortium. ftp://ftp.cogsci.ed.ac. uk/pub/FRACAS/del16.ps.gz.",
"links": null
},
"BIBREF11": {
"ref_id": "b11",
"title": "Word meaning and Montague grammar: The semantics of verbs and times in generative semantics and in Montague's PTQ",
"authors": [
{
"first": "",
"middle": [],
"last": "David R Dowty",
"suffix": ""
}
],
"year": 2012,
"venue": "",
"volume": "7",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "David R Dowty. 2012. Word meaning and Montague grammar: The semantics of verbs and times in gen- erative semantics and in Montague's PTQ, volume 7. Springer Science & Business Media.",
"links": null
},
"BIBREF12": {
"ref_id": "b12",
"title": "The semantics of tense and aspect. The Handbook of Contemporary Semantic Theory",
"authors": [
{
"first": "Tim",
"middle": [],
"last": "Fernando",
"suffix": ""
}
],
"year": 2015,
"venue": "",
"volume": "",
"issue": "",
"pages": "203--236",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Tim Fernando. 2015. The semantics of tense and as- pect. The Handbook of Contemporary Semantic Theory, pages 203-236.",
"links": null
},
"BIBREF13": {
"ref_id": "b13",
"title": "Tense, aspect, and indexicality",
"authors": [
{
"first": "James",
"middle": [],
"last": "Higginbotham",
"suffix": ""
}
],
"year": 2009,
"venue": "OUP Oxford",
"volume": "26",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "James Higginbotham. 2009. Tense, aspect, and indexi- cality, volume 26. OUP Oxford.",
"links": null
},
"BIBREF14": {
"ref_id": "b14",
"title": "A bilingual treebank for the FraCas test suite",
"authors": [
{
"first": "P",
"middle": [],
"last": "Ljungl\u00f6f",
"suffix": ""
},
{
"first": "M",
"middle": [],
"last": "Siverbo",
"suffix": ""
}
],
"year": 2011,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "P. Ljungl\u00f6f and M. Siverbo. 2011. A bilingual treebank for the FraCas test suite. Clt project report, Univer- sity of Gothenburg.",
"links": null
},
"BIBREF15": {
"ref_id": "b15",
"title": "Natural logic for textual inference",
"authors": [
{
"first": "Bill",
"middle": [],
"last": "Maccartney",
"suffix": ""
},
{
"first": "D",
"middle": [],
"last": "Christopher",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Manning",
"suffix": ""
}
],
"year": 2007,
"venue": "Proceedings of the ACL-PASCAL Workshop on Textual Entailment and Paraphrasing",
"volume": "",
"issue": "",
"pages": "193--200",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Bill MacCartney and Christopher D Manning. 2007. Natural logic for textual inference. In Proceedings of the ACL-PASCAL Workshop on Textual Entail- ment and Paraphrasing, pages 193-200. Associa- tion for Computational Linguistics.",
"links": null
},
"BIBREF16": {
"ref_id": "b16",
"title": "Higher-order logical inference with compositional semantics",
"authors": [
{
"first": "Koji",
"middle": [],
"last": "Mineshima",
"suffix": ""
},
{
"first": "Yusuke",
"middle": [],
"last": "Miyao",
"suffix": ""
},
{
"first": "Daisuke",
"middle": [],
"last": "Bekki",
"suffix": ""
}
],
"year": 2015,
"venue": "Proceedings of EMNLP",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Koji Mineshima, Yusuke Miyao, and Daisuke Bekki. 2015. Higher-order logical inference with composi- tional semantics. In Proceedings of EMNLP.",
"links": null
},
"BIBREF17": {
"ref_id": "b17",
"title": "English as a formal language",
"authors": [
{
"first": "Richard",
"middle": [],
"last": "Montague",
"suffix": ""
}
],
"year": 1970,
"venue": "Linguaggi nella Societa e nella Tecnica",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Richard Montague. 1970. English as a formal lan- guage. In Linguaggi nella Societa e nella Tecnica.",
"links": null
},
"BIBREF18": {
"ref_id": "b18",
"title": "The proper treatment of quantification in ordinary english",
"authors": [
{
"first": "Richard",
"middle": [],
"last": "Montague",
"suffix": ""
}
],
"year": 1973,
"venue": "Approaches to natural language",
"volume": "",
"issue": "",
"pages": "221--242",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Richard Montague. 1973. The proper treatment of quantification in ordinary english. In Approaches to natural language, pages 221-242. Springer.",
"links": null
},
"BIBREF19": {
"ref_id": "b19",
"title": "The proper treatment of quantification in ordinary english",
"authors": [
{
"first": "Richard",
"middle": [],
"last": "Montague",
"suffix": ""
}
],
"year": 1974,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Richard Montague. 1974. The proper treatment of quantification in ordinary english. In Richmond Thomason, editor, Formal Philosophy. Yale UP, New Haven.",
"links": null
},
"BIBREF20": {
"ref_id": "b20",
"title": "Tense and aspect in truthconditional semantics",
"authors": [
{
"first": "Toshiyuki",
"middle": [],
"last": "Ogihara",
"suffix": ""
}
],
"year": 2007,
"venue": "Lingua",
"volume": "117",
"issue": "2",
"pages": "392--418",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Toshiyuki Ogihara. 2007. Tense and aspect in truth- conditional semantics. Lingua, 117(2):392-418.",
"links": null
},
"BIBREF21": {
"ref_id": "b21",
"title": "Events in the Semantics of English",
"authors": [
{
"first": "Terence",
"middle": [],
"last": "Parsons",
"suffix": ""
}
],
"year": 1990,
"venue": "",
"volume": "5",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Terence Parsons. 1990. Events in the Semantics of En- glish, volume 5. MIT press Cambridge, MA.",
"links": null
},
"BIBREF22": {
"ref_id": "b22",
"title": "Papers on time and tense",
"authors": [
{
"first": "N",
"middle": [],
"last": "Arthur",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Prior",
"suffix": ""
},
{
"first": "F",
"middle": [
"V"
],
"last": "Per",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Hasle",
"suffix": ""
}
],
"year": 2003,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Arthur N Prior and Per FV Hasle. 2003. Papers on time and tense. Oxford University Press on Demand.",
"links": null
},
"BIBREF23": {
"ref_id": "b23",
"title": "Grammatical framework",
"authors": [
{
"first": "Aarne",
"middle": [],
"last": "Ranta",
"suffix": ""
}
],
"year": 2004,
"venue": "Journal of Functional Programming",
"volume": "14",
"issue": "2",
"pages": "145--189",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Aarne Ranta. 2004. Grammatical framework. Journal of Functional Programming, 14(2):145-189.",
"links": null
},
"BIBREF24": {
"ref_id": "b24",
"title": "The productions of time",
"authors": [
{
"first": "Mark",
"middle": [],
"last": "Steedman",
"suffix": ""
}
],
"year": 2000,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Mark Steedman. 2000. The productions of time. Draft. Available at http://www. cogsci. ed. ac. uk/steedman/papers. html.",
"links": null
},
"BIBREF25": {
"ref_id": "b25",
"title": "Dynamic semantics as monadic computation",
"authors": [
{
"first": "Christina",
"middle": [],
"last": "Unger",
"suffix": ""
}
],
"year": 2011,
"venue": "JSAI International Symposium on Artificial Intelligence",
"volume": "",
"issue": "",
"pages": "68--81",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Christina Unger. 2011. Dynamic semantics as monadic computation. In JSAI International Symposium on Artificial Intelligence, pages 68-81. Springer.",
"links": null
},
"BIBREF26": {
"ref_id": "b26",
"title": "Temporal reasoning in natural language inference",
"authors": [
{
"first": "Siddharth",
"middle": [],
"last": "Vashishtha",
"suffix": ""
},
{
"first": "Adam",
"middle": [],
"last": "Poliak",
"suffix": ""
},
{
"first": "Yash",
"middle": [],
"last": "Kumar Lal",
"suffix": ""
},
{
"first": "Benjamin",
"middle": [],
"last": "Van Durme",
"suffix": ""
},
{
"first": "Aaron",
"middle": [
"Steven"
],
"last": "White",
"suffix": ""
}
],
"year": 2020,
"venue": "Findings of the Association for Computational Linguistics: EMNLP 2020",
"volume": "",
"issue": "",
"pages": "4070--4078",
"other_ids": {
"DOI": [
"10.18653/v1/2020.findings-emnlp.363"
]
},
"num": null,
"urls": [],
"raw_text": "Siddharth Vashishtha, Adam Poliak, Yash Kumar Lal, Benjamin Van Durme, and Aaron Steven White. 2020. Temporal reasoning in natural language infer- ence. In Findings of the Association for Computa- tional Linguistics: EMNLP 2020, pages 4070-4078, Online. Association for Computational Linguistics.",
"links": null
},
"BIBREF27": {
"ref_id": "b27",
"title": "Une th\u00e9orie des constructions inductives",
"authors": [
{
"first": "Benjamin",
"middle": [],
"last": "Werner",
"suffix": ""
}
],
"year": 1994,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Benjamin Werner. 1994. Une th\u00e9orie des constructions inductives. PhD thesis, Universit\u00e9 de Paris 7.",
"links": null
}
},
"ref_entries": {
"FIGREF0": {
"type_str": "figure",
"text": "P1 Smith left after Jones left. P2 Jones left after Anderson left. H Did Smith leave after Anderson left?",
"uris": null,
"num": null
},
"FIGREF1": {
"type_str": "figure",
"text": "))))) -> Not (exists (f: Time), ((exists (g: Time),",
"uris": null,
"num": null
}
}
}
} |