380:
210:
375:{\displaystyle \langle e,t\rangle ;\qquad \langle t,t\rangle ;\qquad \langle \langle e,t\rangle ,t\rangle ;\qquad \langle e,\langle e,t\rangle \rangle ;\qquad \langle \langle e,t\rangle ,\langle \langle e,t\rangle ,t\rangle \rangle ;\qquad \ldots }
845:
105:
1307:
1699:
1449:
938:
891:
1921:
1067:
1217:
1836:
1361:
1173:
775:
741:
622:
520:
184:
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563:
1611:
1517:
1387:
986:
1131:
473:
1098:
418:
662:
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782:
946:
to a function from a set to a truth value. Put differently, it denotes a function from a set to a set of sets. It is that function which for any two sets
1752:
The first sentence does not entail the second. The fact that the number of students that ran is exactly three does not entail that each of these students
49:
1478:
1951:
2084:
2007:
1244:
573:. They map every individual that is an element of the set to "true", and everything else to "false." It is common to say that they denote
1654:
1069:
Such lambda terms are functions whose domain is what precedes the period, and whose range are the type of thing that follows the period. If
2894:
1858:
1756:, so the number of students that did that can be smaller than 3. Conversely, the second sentence does not entail the first. The sentence
577:
rather than characteristic functions, although, strictly speaking, the latter is more accurate. Examples of expressions of this type are
2198:
1178:
2672:
1781:
1015:
128:
is often used to make the semantics of different kinds of expressions explicit. The standard construction defines the set of types
1316:
2149:
2115:
2096:
2028:
1410:
899:
852:
2540:
2207:
2170:
20:
475:, where 0 stands for "false" and 1 stands for "true". Examples of expressions that are sometimes said to be of type
1366:
2627:
1107:
1942:
is not conservative. The following two sentences are not equivalent. But it is, in fact, not common to analyze
2748:
2622:
2281:
2191:
2006:(1974). "The proper treatment of quantification in English". In Kulas, J.; Fetzer, J.H.; Rankin, T.L. (eds.).
2400:
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can be true, even though the number of students who merely ran (i.e. not so fast) is greater than 3.
1648:
2833:
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2271:
1974:
1947:
1764:
1641:
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529:
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1979:
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2410:
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1702:
523:
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1310:
446:
390:
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2324:
1984:
1076:
396:
707:
We can now assign types to the words in our sentence above (Every boy sleeps) as follows.
526:
from the set of entities to the set of truth values. This set of functions is rendered as
8:
2823:
2788:
2733:
2677:
2580:
2565:
2535:
2515:
2490:
2359:
2344:
2108:
Quantifiers in Action: Generalized
Quantification in Query, Logical and Natural Languages
2051:
1737:
if it is neither monotone increasing nor monotone decreasing. An example of such a GQ is
1568:
1474:
840:{\displaystyle \langle \langle e,t\rangle ,\langle \langle e,t\rangle ,t\rangle \rangle }
578:
2889:
2868:
2793:
2763:
2728:
2708:
2637:
2617:
2555:
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2460:
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2435:
2379:
1572:
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36:
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188:
Nothing is a type, except what can be constructed on the basis of lines 1 and 2 above.
2848:
2803:
2783:
2743:
2682:
2652:
2632:
2425:
2354:
2145:
2111:
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2024:
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570:
2015:. Studies in Cognitive Systems. Vol. 2. Springer, Dordrecht. pp. 141–162.
2853:
2778:
2667:
2445:
2135:
2063:
2016:
2003:
110:
2657:
2560:
2455:
2420:
997:
2020:
2843:
2838:
2758:
2642:
2520:
2415:
2256:
1846:
2883:
2530:
2505:
2339:
393:, the set of entities the discourse is about. This set is usually written as
2126:
896:
and so we can see that the generalized quantifier in our example is of type
2798:
2718:
2585:
2465:
2349:
2329:
2140:
1004:
as the following lambda expression, which is a function from an individual
2713:
2687:
2570:
2334:
2261:
2047:
1771:
440:
125:
39:
32:
1938:
determiners—in every natural language—are conservative. The expression
1629:. For this GQ we have that the first sentence below entails the second.
2863:
2510:
2276:
2231:
2226:
2067:
1548:
1524:
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2480:
2405:
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2314:
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1701:
Monotone decreasing GQs are among the expressions that can license a
586:
201:
129:
113:
2575:
2364:
204:
1709:. Monotone increasing GQs do not license negative polarity items.
100:{\displaystyle \{X\mid \forall x(x{\text{ is a boy}}\to x\in X)\}}
109:
This treatment of quantifiers has been essential in achieving a
1954:
2440:
2083:
1539:
is monotone increasing. For example, the set of things that
1400:
582:
1647:
is the following. It says that the two sets have an empty
1923:
For example, the following two sentences are equivalent.
1741:. Neither of the following sentences entails the other.
1302:{\displaystyle (\lambda X.\lambda Y.X\subseteq Y)(B)(S)}
46:
denotes the set of sets of which every boy is a member:
2206:
1694:{\displaystyle \lambda X.\lambda Y.X\cap Y=\emptyset }
1861:
1784:
1657:
1593:
1499:
1444:{\displaystyle \langle \langle e,t\rangle ,t\rangle }
1413:
1369:
1319:
1247:
1181:
1149:
1110:
1079:
1018:
968:
933:{\displaystyle \langle \langle e,t\rangle ,t\rangle }
902:
886:{\displaystyle \langle \langle e,t\rangle ,t\rangle }
855:
785:
751:
717:
670:
650:
630:
598:
532:
496:
449:
399:
213:
160:
52:
16:
Expression denoting a set of sets in formal semantics
1916:{\displaystyle D(A)(B)\leftrightarrow D(A)(A\cap B)}
1915:
1830:
1693:
1605:
1511:
1443:
1381:
1355:
1301:
1211:
1167:
1125:
1092:
1061:
980:
932:
885:
839:
769:
735:
695:
656:
636:
624:denote functions from the set of entities of type
616:
557:
514:
467:
412:
374:
178:
99:
2009:Philosophy, Language, and Artificial Intelligence
2881:
2673:Segmented discourse representation theory (SDRT)
1212:{\displaystyle \lambda X.\lambda Y.X\subseteq Y}
192:Given this definition, we have the simple types
1831:{\displaystyle \lambda X.\lambda Y.|X\cap Y|=3}
996:A useful way to write complex functions is the
2052:"Generalized quantifiers and natural language"
1062:{\displaystyle \lambda x.\mathrm {sleep} '(x)}
35:. This is the standard semantics assigned to
2192:
2105:
2046:
1100:, then the following lambda term denotes the
1438:
1429:
1417:
1414:
1162:
1150:
1000:. For example, one can write the meaning of
927:
918:
906:
903:
880:
871:
859:
856:
834:
831:
822:
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807:
801:
789:
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611:
599:
509:
497:
462:
450:
362:
359:
350:
338:
335:
329:
317:
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292:
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267:
255:
252:
245:
233:
226:
214:
173:
161:
94:
53:
1356:{\displaystyle (\lambda Y.B\subseteq Y)(S)}
1237:", respectively, we have that the sentence
1073:is a variable that ranges over elements of
2199:
2185:
1625:An example of a monotone decreasing GQ is
1562:
1464:
42:. For example, the generalized quantifier
2139:
2042:
2040:
592:In general, expressions of complex types
207:of complex types, some of which include:
2002:
1950:. Rather, it is standardly treated as a
991:
664:, a construct we can write as follows:
2882:
2124:
2037:
1547:. Therefore, the first sentence below
1543:is a subset of the set of things that
1139:with the following lambda term, where
942:Thus, every denotes a function from a
116:for sentences containing quantifiers.
2628:Discourse representation theory (DRT)
2180:
1855:if the following equivalence holds:
2895:Formal semantics (natural language)
2541:Quantificational variability effect
2208:Formal semantics (natural language)
2171:Stanford Encyclopedia of Philosophy
1770:is the following. It says that the
1728:
1168:{\displaystyle \langle e,t\rangle }
770:{\displaystyle \langle e,t\rangle }
736:{\displaystyle \langle e,t\rangle }
617:{\displaystyle \langle a,b\rangle }
515:{\displaystyle \langle e,t\rangle }
179:{\displaystyle \langle a,b\rangle }
13:
2134:. Berlin: Language Science Press.
2077:
1763:The lambda term for the (complex)
1688:
1042:
1039:
1036:
1033:
1030:
62:
31:) is an expression that denotes a
14:
2911:
2159:
2089:Quantifiers in language and logic
1840:
1748:Exactly three students ran fast.
1221:If we abbreviate the meaning of
1135:We can now write the meaning of
1778:between the two sets equals 3.
1758:exactly three students ran fast
1459:
644:to the set of entities of type
368:
313:
282:
251:
232:
2623:Combinatory categorial grammar
1996:
1930:Every boy is a boy who sleeps.
1910:
1898:
1895:
1889:
1883:
1880:
1874:
1871:
1865:
1818:
1804:
1350:
1344:
1341:
1320:
1296:
1290:
1287:
1281:
1278:
1248:
1056:
1050:
443:, usually rendered as the set
119:
91:
79:
68:
1:
2401:Antecedent-contained deletion
1990:
1964:Only boys are boys who sleep.
1851:A determiner D is said to be
1575:) if, for every pair of sets
1481:) if, for every pair of sets
1454:
696:{\displaystyle D_{b}^{D_{a}}}
558:{\displaystyle D_{t}^{D_{e}}}
1606:{\displaystyle X\subseteq Y}
1512:{\displaystyle X\subseteq Y}
1382:{\displaystyle B\subseteq S}
981:{\displaystyle A\subseteq B}
7:
2021:10.1007/978-94-009-2727-8_7
1968:
1745:Exactly three students ran.
1126:{\displaystyle \lambda x.x}
154:are both types, then so is
10:
2916:
2282:Syntax–semantics interface
2087:; Dag WesterstĂĄhl (2006).
2056:Linguistics and Philosophy
1934:It has been proposed that
1844:
2816:
2774:Question under discussion
2724:Conversational scoreboard
2701:
2605:
2598:
2501:Intersective modification
2486:Homogeneity (linguistics)
2393:
2302:
2295:
2214:
1241:now means the following:
2834:Distributional semantics
2165:Dag WesterstĂĄhl, 2011. '
2128:Subatomic quantification
2050:; Cooper, Robin (1981).
1975:Scope (formal semantics)
1640:The lambda term for the
1008:to the proposition that
567:characteristic functions
2829:Computational semantics
2566:Subsective modification
2370:Propositional attitudes
2167:Generalized Quantifiers
1583:, the following holds:
1563:Monotone decreasing GQs
1489:, the following holds:
1465:Monotone increasing GQs
468:{\displaystyle \{0,1\}}
389:denote elements of the
2859:Philosophy of language
2496:Inalienable possession
2476:Free choice inferences
2471:Faultless disagreement
2242:Generalized quantifier
2141:10.5281/zenodo.5106382
2106:Antonio Badia (2009).
1917:
1832:
1703:negative polarity item
1695:
1607:
1513:
1471:generalized quantifier
1445:
1405:generalized quantifier
1383:
1357:
1303:
1213:
1169:
1143:are variables of type
1127:
1094:
1063:
982:
934:
887:
841:
771:
737:
697:
658:
638:
618:
559:
516:
469:
414:
376:
180:
101:
25:generalized quantifier
2754:Plural quantification
2648:Inquisitive semantics
2613:Alternative semantics
1918:
1845:Further information:
1833:
1696:
1608:
1514:
1446:
1384:
1358:
1304:
1214:
1170:
1128:
1095:
1093:{\displaystyle D_{e}}
1064:
992:Typed lambda calculus
983:
935:
888:
842:
772:
738:
698:
659:
639:
619:
565:. Such functions are
560:
517:
470:
415:
413:{\displaystyle D_{e}}
391:universe of discourse
377:
181:
102:
2739:Function application
2546:Responsive predicate
2536:Privative adjectives
1985:Branching quantifier
1980:Lindström quantifier
1859:
1782:
1720:Bad: *Every boy has
1655:
1591:
1555:Every boy runs fast.
1497:
1411:
1367:
1317:
1245:
1179:
1147:
1108:
1077:
1016:
966:
962:)= 1 if and only if
900:
853:
783:
749:
715:
668:
648:
628:
596:
530:
494:
490:Expressions of type
447:
435:Expressions of type
424:expressions include
420:. Examples of type
397:
385:Expressions of type
211:
158:
50:
2824:Cognitive semantics
2789:Strawson entailment
2734:Existential closure
2678:Situation semantics
2581:Temperature paradox
2551:Rising declaratives
2516:Modal subordination
2491:Hurford disjunction
2451:Discourse relations
2091:. Clarendon Press.
1733:A GQ is said to be
1569:monotone decreasing
1567:A GQ is said to be
1475:monotone increasing
692:
554:
2900:Quantifier (logic)
2869:Semantics of logic
2794:Strict conditional
2764:Quantifier raising
2729:Downward entailing
2709:Autonomy of syntax
2638:Generative grammar
2618:Categorial grammar
2556:Scalar implicature
2461:Epistemic modality
2436:De dicto and de re
2068:10.1007/BF00350139
1913:
1828:
1739:exactly three boys
1691:
1603:
1573:downward entailing
1509:
1441:
1399:. Combined with a
1379:
1353:
1299:
1209:
1165:
1123:
1090:
1059:
978:
930:
883:
849:Type(every boy) =
837:
767:
733:
693:
671:
654:
634:
614:
585:and some kinds of
555:
533:
512:
465:
410:
372:
176:
97:
2877:
2876:
2849:Logic translation
2812:
2811:
2804:Universal grinder
2784:Squiggle operator
2744:Meaning postulate
2683:Supervaluationism
2653:Intensional logic
2633:Dynamic semantics
2594:
2593:
2426:Crossover effects
2375:Tense–aspect–mood
2355:Lexical semantics
2151:978-3-98554-011-2
2125:WÄ…giel M (2021).
2117:978-0-387-09563-9
2098:978-0-19-929125-0
2030:978-94-010-7726-2
2004:Montague, Richard
1927:Every boy sleeps.
1713:Good: No boy has
1636:No boy runs fast.
1473:GQ is said to be
1102:identity function
657:{\displaystyle b}
637:{\displaystyle a}
77:
2907:
2854:Linguistics wars
2779:Semantic parsing
2668:Montague grammar
2603:
2602:
2446:Deontic modality
2300:
2299:
2287:Truth conditions
2222:Compositionality
2215:Central concepts
2201:
2194:
2187:
2178:
2177:
2155:
2143:
2133:
2121:
2102:
2072:
2071:
2044:
2035:
2034:
2014:
2000:
1961:Only boys sleep.
1922:
1920:
1919:
1914:
1837:
1835:
1834:
1829:
1821:
1807:
1729:Non-monotone GQs
1700:
1698:
1697:
1692:
1612:
1610:
1609:
1604:
1518:
1516:
1515:
1510:
1479:upward entailing
1450:
1448:
1447:
1442:
1388:
1386:
1385:
1380:
1362:
1360:
1359:
1354:
1308:
1306:
1305:
1300:
1239:every boy sleeps
1218:
1216:
1215:
1210:
1174:
1172:
1171:
1166:
1132:
1130:
1129:
1124:
1104:on individuals:
1099:
1097:
1096:
1091:
1089:
1088:
1068:
1066:
1065:
1060:
1049:
1045:
987:
985:
984:
979:
939:
937:
936:
931:
892:
890:
889:
884:
846:
844:
843:
838:
776:
774:
773:
768:
742:
740:
739:
734:
702:
700:
699:
694:
691:
690:
689:
679:
663:
661:
660:
655:
643:
641:
640:
635:
623:
621:
620:
615:
564:
562:
561:
556:
553:
552:
551:
541:
521:
519:
518:
513:
474:
472:
471:
466:
419:
417:
416:
411:
409:
408:
381:
379:
378:
373:
185:
183:
182:
177:
106:
104:
103:
98:
78:
75:
21:formal semantics
2915:
2914:
2910:
2909:
2908:
2906:
2905:
2904:
2880:
2879:
2878:
2873:
2808:
2697:
2658:Lambda calculus
2590:
2561:Sloppy identity
2521:Opaque contexts
2456:Donkey anaphora
2421:Counterfactuals
2389:
2291:
2210:
2205:
2162:
2152:
2131:
2118:
2099:
2080:
2078:Further reading
2075:
2045:
2038:
2031:
2012:
2001:
1997:
1993:
1971:
1952:focus-sensitive
1860:
1857:
1856:
1849:
1843:
1817:
1803:
1783:
1780:
1779:
1731:
1656:
1653:
1652:
1592:
1589:
1588:
1565:
1558:Every boy runs.
1498:
1495:
1494:
1467:
1462:
1457:
1412:
1409:
1408:
1391:The expression
1368:
1365:
1364:
1318:
1315:
1314:
1246:
1243:
1242:
1180:
1177:
1176:
1148:
1145:
1144:
1109:
1106:
1105:
1084:
1080:
1078:
1075:
1074:
1029:
1028:
1017:
1014:
1013:
998:lambda calculus
994:
967:
964:
963:
901:
898:
897:
854:
851:
850:
784:
781:
780:
750:
747:
746:
745:Type(sleeps) =
716:
713:
712:
685:
681:
680:
675:
669:
666:
665:
649:
646:
645:
629:
626:
625:
597:
594:
593:
547:
543:
542:
537:
531:
528:
527:
495:
492:
491:
448:
445:
444:
404:
400:
398:
395:
394:
212:
209:
208:
159:
156:
155:
122:
74:
51:
48:
47:
17:
12:
11:
5:
2913:
2903:
2902:
2897:
2892:
2875:
2874:
2872:
2871:
2866:
2861:
2856:
2851:
2846:
2844:Inferentialism
2841:
2839:Formal grammar
2836:
2831:
2826:
2820:
2818:
2814:
2813:
2810:
2809:
2807:
2806:
2801:
2796:
2791:
2786:
2781:
2776:
2771:
2766:
2761:
2759:Possible world
2756:
2751:
2746:
2741:
2736:
2731:
2726:
2721:
2716:
2711:
2705:
2703:
2699:
2698:
2696:
2695:
2690:
2685:
2680:
2675:
2670:
2665:
2660:
2655:
2650:
2645:
2643:Glue semantics
2640:
2635:
2630:
2625:
2620:
2615:
2609:
2607:
2606:Formal systems
2600:
2596:
2595:
2592:
2591:
2589:
2588:
2583:
2578:
2573:
2568:
2563:
2558:
2553:
2548:
2543:
2538:
2533:
2531:Polarity items
2528:
2523:
2518:
2513:
2508:
2503:
2498:
2493:
2488:
2483:
2478:
2473:
2468:
2463:
2458:
2453:
2448:
2443:
2438:
2433:
2428:
2423:
2418:
2416:Conservativity
2413:
2408:
2403:
2397:
2395:
2391:
2390:
2388:
2387:
2382:
2380:Quantification
2377:
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2327:
2322:
2317:
2312:
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2304:
2297:
2293:
2292:
2290:
2289:
2284:
2279:
2274:
2269:
2264:
2259:
2257:Presupposition
2254:
2249:
2244:
2239:
2234:
2229:
2224:
2218:
2216:
2212:
2211:
2204:
2203:
2196:
2189:
2181:
2175:
2174:
2161:
2160:External links
2158:
2157:
2156:
2150:
2122:
2116:
2103:
2097:
2085:Stanley Peters
2079:
2076:
2074:
2073:
2062:(2): 159–219.
2036:
2029:
1994:
1992:
1989:
1988:
1987:
1982:
1977:
1970:
1967:
1966:
1965:
1962:
1932:
1931:
1928:
1912:
1909:
1906:
1903:
1900:
1897:
1894:
1891:
1888:
1885:
1882:
1879:
1876:
1873:
1870:
1867:
1864:
1847:Conservativity
1842:
1841:Conservativity
1839:
1827:
1824:
1820:
1816:
1813:
1810:
1806:
1802:
1799:
1796:
1793:
1790:
1787:
1750:
1749:
1746:
1730:
1727:
1726:
1725:
1718:
1690:
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1681:
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1669:
1666:
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1660:
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1634:
1623:
1622:
1602:
1599:
1596:
1564:
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1560:
1559:
1556:
1533:
1532:
1508:
1505:
1502:
1466:
1463:
1461:
1458:
1456:
1453:
1440:
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1431:
1428:
1425:
1422:
1419:
1416:
1403:, it yields a
1378:
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1352:
1349:
1346:
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1340:
1337:
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1331:
1328:
1325:
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1280:
1277:
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1268:
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1262:
1259:
1256:
1253:
1250:
1208:
1205:
1202:
1199:
1196:
1193:
1190:
1187:
1184:
1164:
1161:
1158:
1155:
1152:
1122:
1119:
1116:
1113:
1087:
1083:
1058:
1055:
1052:
1048:
1044:
1041:
1038:
1035:
1032:
1027:
1024:
1021:
993:
990:
977:
974:
971:
929:
926:
923:
920:
917:
914:
911:
908:
905:
894:
893:
882:
879:
876:
873:
870:
867:
864:
861:
858:
847:
836:
833:
830:
827:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
779:Type(every) =
777:
766:
763:
760:
757:
754:
743:
732:
729:
726:
723:
720:
705:
704:
688:
684:
678:
674:
653:
633:
613:
610:
607:
604:
601:
590:
550:
546:
540:
536:
511:
508:
505:
502:
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464:
461:
458:
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452:
433:
407:
403:
371:
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361:
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228:
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175:
172:
169:
166:
163:
144:
121:
118:
96:
93:
90:
87:
84:
81:
76: is a boy
73:
70:
67:
64:
61:
58:
55:
15:
9:
6:
4:
3:
2:
2912:
2901:
2898:
2896:
2893:
2891:
2888:
2887:
2885:
2870:
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2865:
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2529:
2527:
2526:Performatives
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2522:
2519:
2517:
2514:
2512:
2509:
2507:
2506:Logophoricity
2504:
2502:
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2340:Evidentiality
2338:
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2213:
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2065:
2061:
2057:
2053:
2049:
2043:
2041:
2032:
2026:
2022:
2018:
2011:
2010:
2005:
1999:
1995:
1986:
1983:
1981:
1978:
1976:
1973:
1972:
1963:
1960:
1959:
1958:
1956:
1953:
1949:
1945:
1941:
1937:
1929:
1926:
1925:
1924:
1907:
1904:
1901:
1892:
1886:
1877:
1868:
1862:
1854:
1848:
1838:
1825:
1822:
1814:
1811:
1808:
1800:
1797:
1794:
1791:
1788:
1785:
1777:
1773:
1769:
1768:exactly three
1766:
1761:
1759:
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1747:
1744:
1743:
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1740:
1736:
1723:
1719:
1716:
1712:
1711:
1710:
1708:
1704:
1685:
1682:
1679:
1676:
1673:
1670:
1667:
1664:
1661:
1658:
1650:
1646:
1643:
1635:
1632:
1631:
1630:
1628:
1620:
1617:) entails GQ(
1616:
1600:
1597:
1594:
1586:
1585:
1584:
1582:
1578:
1574:
1571:(also called
1570:
1557:
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1552:
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1530:
1526:
1522:
1506:
1503:
1500:
1492:
1491:
1490:
1488:
1484:
1480:
1477:(also called
1476:
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1435:
1432:
1426:
1423:
1420:
1406:
1402:
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1323:
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1275:
1272:
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1219:
1206:
1203:
1200:
1197:
1194:
1191:
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1159:
1156:
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1142:
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1133:
1120:
1117:
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1111:
1103:
1085:
1081:
1072:
1053:
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1007:
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953:
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828:
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778:
761:
758:
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727:
724:
721:
710:
709:
708:
686:
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672:
651:
631:
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568:
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500:
489:
486:
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478:
459:
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438:
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347:
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326:
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295:
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279:
273:
270:
264:
261:
258:
248:
242:
239:
236:
229:
223:
220:
217:
206:
203:
200:, but also a
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195:
187:
170:
167:
164:
153:
149:
145:
142:
138:
135:
134:
133:
131:
127:
124:A version of
117:
115:
112:
111:compositional
107:
88:
85:
82:
71:
65:
59:
56:
45:
41:
38:
34:
30:
26:
22:
2799:Type shifter
2769:Quantization
2719:Continuation
2586:Veridicality
2466:Exhaustivity
2431:Cumulativity
2350:Indexicality
2330:Definiteness
2325:Conditionals
2252:Logical form
2241:
2127:
2110:. Springer.
2107:
2088:
2059:
2055:
2048:Barwise, Jon
2008:
1998:
1943:
1939:
1935:
1933:
1853:conservative
1852:
1850:
1776:intersection
1767:
1762:
1757:
1753:
1751:
1738:
1735:non-monotone
1734:
1732:
1721:
1714:
1706:
1649:intersection
1644:
1639:
1633:No boy runs.
1626:
1624:
1618:
1614:
1580:
1576:
1566:
1551:the second:
1544:
1540:
1536:
1534:
1528:
1520:
1486:
1482:
1470:
1468:
1460:Monotonicity
1404:
1392:
1390:
1238:
1234:
1230:
1226:
1222:
1220:
1140:
1136:
1134:
1070:
1009:
1005:
1001:
995:
959:
955:
951:
947:
943:
941:
895:
711:Type(boy) =
706:
574:
485:propositions
484:
480:
476:
436:
429:
425:
421:
386:
197:
193:
191:
151:
147:
140:
136:
132:as follows:
123:
108:
43:
40:noun phrases
28:
24:
18:
2714:Context set
2688:Type theory
2571:Subtrigging
2335:Disjunction
2262:Proposition
1772:cardinality
1311:β-reduction
441:truth value
130:recursively
126:type theory
120:Type theory
33:set of sets
2884:Categories
2864:Pragmatics
2511:Mirativity
2277:Speech act
2232:Entailment
2227:Denotation
1991:References
1948:determiner
1765:determiner
1705:, such as
1642:determiner
1613:, then GQ(
1519:, then GQ(
1455:Properties
1397:determiner
587:adjectives
579:predicates
143:are types.
37:quantified
2890:Semantics
2663:Mereology
2599:Formalism
2481:Givenness
2406:Cataphora
2394:Phenomena
2385:Vagueness
2315:Ambiguity
2267:Reference
2247:Intension
2237:Extension
1905:∩
1884:↔
1812:∩
1795:λ
1786:λ
1689:∅
1680:∩
1668:λ
1659:λ
1598:⊆
1537:every boy
1504:⊆
1439:⟩
1430:⟩
1418:⟨
1415:⟨
1374:⊆
1336:⊆
1324:λ
1273:⊆
1261:λ
1252:λ
1204:⊆
1192:λ
1183:λ
1163:⟩
1151:⟨
1112:λ
1020:λ
973:⊆
928:⟩
919:⟩
907:⟨
904:⟨
881:⟩
872:⟩
860:⟨
857:⟨
835:⟩
832:⟩
823:⟩
811:⟨
808:⟨
802:⟩
790:⟨
787:⟨
765:⟩
753:⟨
731:⟩
719:⟨
612:⟩
600:⟨
524:functions
510:⟩
498:⟨
481:sentences
439:denote a
370:…
363:⟩
360:⟩
351:⟩
339:⟨
336:⟨
330:⟩
318:⟨
315:⟨
308:⟩
305:⟩
293:⟨
284:⟨
277:⟩
268:⟩
256:⟨
253:⟨
246:⟩
234:⟨
227:⟩
215:⟨
202:countable
174:⟩
162:⟨
114:semantics
86:∈
80:→
63:∀
60:∣
44:every boy
2817:See also
2702:Concepts
2576:Telicity
2411:Coercion
2365:Negation
2360:Modality
2310:Anaphora
1969:See also
1754:ran fast
1541:run fast
1407:of type
1047:′
1010:x sleeps
205:infinity
2320:Binding
1774:of the
1549:entails
1535:The GQ
1525:entails
1233:" and "
522:denote
2749:Monads
2296:Topics
2148:
2114:
2095:
2027:
1955:adverb
1724:money.
1717:money.
1627:no boy
1227:sleeps
1002:sleeps
2441:De se
2345:Focus
2303:Areas
2272:Scope
2132:(pdf)
2013:(PDF)
1946:as a
1395:is a
1393:every
1137:every
952:every
583:nouns
2169:'.
2146:ISBN
2112:ISBN
2093:ISBN
2025:ISBN
1944:only
1940:only
1579:and
1485:and
1401:noun
1363:and
1229:as "
1225:and
575:sets
571:sets
479:are
428:and
426:John
196:and
150:and
139:and
23:, a
2693:TTR
2136:doi
2064:doi
2017:doi
1936:all
1722:any
1715:any
1707:any
1587:If
1545:run
1527:GQ(
1493:if
1309:By
1223:boy
1141:X,Y
948:A,B
944:set
569:of
483:or
146:If
19:In
2886::
2144:.
2058:.
2054:.
2039:^
2023:.
1957:.
1651:.
1645:no
1621:).
1531:).
1523:)
1469:A
1451:.
1313:,
1175::
1012:.
988:.
958:)(
950:,
581:,
430:he
29:GQ
2200:e
2193:t
2186:v
2173:.
2154:.
2138::
2120:.
2101:.
2070:.
2066::
2060:4
2033:.
2019::
1911:)
1908:B
1902:A
1899:(
1896:)
1893:A
1890:(
1887:D
1881:)
1878:B
1875:(
1872:)
1869:A
1866:(
1863:D
1826:3
1823:=
1819:|
1815:Y
1809:X
1805:|
1801:.
1798:Y
1792:.
1789:X
1686:=
1683:Y
1677:X
1674:.
1671:Y
1665:.
1662:X
1619:X
1615:Y
1601:Y
1595:X
1581:Y
1577:X
1529:Y
1521:X
1507:Y
1501:X
1487:Y
1483:X
1436:t
1433:,
1427:t
1424:,
1421:e
1377:S
1371:B
1351:)
1348:S
1345:(
1342:)
1339:Y
1333:B
1330:.
1327:Y
1321:(
1297:)
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1291:(
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1279:)
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1270:X
1267:.
1264:Y
1258:.
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1249:(
1235:S
1231:B
1207:Y
1201:X
1198:.
1195:Y
1189:.
1186:X
1160:t
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1154:e
1121:x
1118:.
1115:x
1086:e
1082:D
1071:x
1057:)
1054:x
1051:(
1043:p
1040:e
1037:e
1034:l
1031:s
1026:.
1023:x
1006:x
976:B
970:A
960:B
956:A
954:(
925:t
922:,
916:t
913:,
910:e
878:t
875:,
869:t
866:,
863:e
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826:,
820:t
817:,
814:e
805:,
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796:,
793:e
762:t
759:,
756:e
728:t
725:,
722:e
703:.
687:a
683:D
677:b
673:D
652:b
632:a
609:b
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603:a
589:.
549:e
545:D
539:t
535:D
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487:.
477:t
463:}
460:1
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366:;
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327:t
324:,
321:e
311:;
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299:,
296:e
290:,
287:e
280:;
274:t
271:,
265:t
262:,
259:e
249:;
243:t
240:,
237:t
230:;
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218:e
198:t
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171:b
168:,
165:a
152:b
148:a
141:t
137:e
95:}
92:)
89:X
83:x
72:x
69:(
66:x
57:X
54:{
27:(
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