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Scope (formal semantics)

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128:(non-split) reading, this sentence means that there is no employee such that the company needs to fire that employee. This is a non-split scope reading since "no" simply takes scope above the modal "need". On the split scope reading of this sentence, it means that it is not the case that the company needs to fire any employees. On this reading, "no" decomposes into a negation scoping above "need" and an 358:
to govern scopal relations. Since type shifters are applied during the process of semantic interpretation, this approach allows scopal relations to be partly independent of syntactic structure. The type shifting approach serves as the basis of many recent proposals for exceptional scope, split scope,
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While operators can often take scope above their surface position, there are not entirely free to take scope wherever they want. For instance, as illustrated by Sentence 1 below, quantifiers that originate inside an if-clause usually cannot take scope outside of that "if"-clause. This sentence cannot
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While most operators are unable to scope out of an island, others can. For instance, the indefinite "a" in the sentence below can take scope outside of its surface position inside an "if"-clause. This sentence can mean that there is a particular relative who must die for the speaker to get a house.
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Among this sentence's reading is one which means "There exists a set of three relatives such that, if those three relatives die, I will inherit a house." On this reading, the indefinite "three relatives of mine" takes existential scope outside the conditional–– it asserts unconditionally that those
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This noun phrase is felicitous to use in this context, even though there is no unique hat. What seems to license this surprising use of the definite description is the fact that the context contains a unique rabbit-containing hat. To cash out this idea, it has been proposed that the uniqueness
275:. Recent work such as Charlow (2020) treats indefinites as denoting sets of individuals which can be type shifted so that they take scope in a manner similar to Karttunen's (1977) alternative-based mechanism for wh-questions. 115:
Split scope is the phenomenon where different components of an expressions item's meaning take scope in different places. Negative quantifiers are one category of expression which have been argued to take split scope.
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Aside from their theoretical significance, scope islands are also practically useful since they can be used to construct unambiguous paraphrases of sentences with scope ambiguities.
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three relatives do in fact exist. However, it the indefinite takes distributive scope inside the conditional–– the speaker will inherit a house if three relatives die, not if
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is one influential view which posits a close relationship between syntax and semantics. This approach is characterized by the following hypothesis, first formulated by
1112: 339:. The movement approach is motivated in large part by the fact that quantifier scope seems to obey many of the same restrictions that movement does, e.g. 1871: 174:
in a context where there are multiple cats which the speaker could have in mind. However, this generalization seems to be contradicted by
312:: The semantic scope of an operator corresponds to the position of the item which expresses it at some level of syntactic representation. 1075:; Rooth, Mats (1983). "Generalized conjunction and type ambiguity". In von Stechow, Arnim; Schwarze, Christoph; Bauerle, Rainer (eds.). 1175: 1649: 50:
and their semantic scope. This relationship is not transparent, since the scope of an operator need not directly correspond to its
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proposed another choice function-based theory, which is similar to Reinhart's except that the choice function variable is left
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In structural approaches, discrepancies between an expression's surface position and its semantic scope are explained by
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Examples of this sort have been used to argue that scope relations are determined by syntactic movement operations.
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presupposition of "the hat" takes scope separately from the rest of the definite's meaning. In other words, a
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approaches such as that of Heim and Kratzer (1998). In these approaches, the relevant syntactic level is
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between different scope construals. Some theories of scope posit a level of syntactic structure called
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Reinhart, Tanya (1997). "Quantifier scope: How labor is divided between QR and choice functions".
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of a semantic operator is the semantic object to which it applies. For instance, in the sentence "
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One of the major concerns of research in formal semantics is the relationship between operators'
39:, but the proposition that Paulina drinks wine does not. Scope can be thought of as the semantic 1033: 731: 688: 508: 1830: 1502: 1472: 1447: 1387: 1286: 1218: 381: 256: 129: 812:. Studies in Linguistics and Philosophy. Vol. 70. Dordrecht: Springer. pp. 163–196. 808:(1998). "Scope or pseudoscope? Are there wide-scope indefinites?". In Rothstein, Susan (ed.). 1730: 1624: 1589: 1477: 1452: 1296: 1213: 190: 171: 163: 107:
reading, the sentence can be true even if the hedgehogs are friends with different giraffes.
1861: 1715: 1522: 1301: 340: 987: 939:(1979). "Syntactic domains for semantic rules". In GĂĽnthner, Franz; Schmidt, J.S. (eds.). 642: 438: 8: 1795: 1710: 1654: 1557: 1542: 1512: 1492: 1467: 1336: 1321: 103:
reading, there is a single giraffe who is very popular in the hedgehog community. On the
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and the syntactic notion which corresponds to semantic scope is typically identified as
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that their referents are unique. For instance, the definite description "the cat" is
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Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers
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Examples of this sort have been used to argue that indefinites do not have standard
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Context: In front of the speaker are numerous hats, one of which contains a rabbit.
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have also been argued to have split scope. Definites are classically considered to
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Proceedings of The 10th International Joint Conference on Artificial Intelligence
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is establishes low in the structure, but is checked for singletonness higher up.
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in that the relative scopes of two operators can be construed in multiple ways.
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of the sentence it occurs in. For instance, some sentences display a
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Indefinites have been argued to have split scope, having separate
1118:. In Groenendijk, Jeroen; de Jong, Dick; Stokhof, Martin (eds.). 286: 624:"Incremental interpretation and Combinatory Categorial Grammar" 47: 880:
Karttunen, Lauri (1977). "Syntax and semantics of questions".
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mean that Beth will inherit one house for each dead relative.
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The scope of an operator need not correspond directly to the
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One prominent alternative to the structural view is the
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This fact parallels the fact that a wh-phrase cannot be
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If every relative of mine dies, I will inherit a house.
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If three relatives of mine die, I will inherit a house.
997:(2 ed.). Dordrecht: Springer. pp. 159–225. 941:
Formal Semantics and Pragmatics for Natural Languages
448:(2 ed.). Dordrecht: Springer. pp. 159–225. 99:
This sentence can be understood in two ways. On the
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that Paulina drinks beer occurs within the scope of
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If a relative of mine dies, I will inherit a house.
143:. This fact can be seen in the following example: 29:Paulina doesn't drink beer but she does drink wine 1853: 1650:Segmented discourse representation theory (SDRT) 652:(2 ed.). Dordrecht: Springer. Section 3.2. 1043:(2 ed.). Wiley Blackwell. pp. 40–76. 359:and other troublesome scope-related phenomena. 1169: 281: 214:from an "if"-clause, as shown in Sentence 2. 1077:Meaning, Use, and Interpretation of Language 975:. Oxford: Wiley Blackwell. pp. 184–188. 698:(2 ed.). Wiley Blackwell. Section 1.6. 518:(2 ed.). Wiley Blackwell. Section 4.3. 426:. Oxford: Wiley Blackwell. pp. 194–198. 16:Semantic object to which an operator applies 1071: 993:. In Gabbay, Dov; Guenthner, Franz (eds.). 963: 648:. In Gabbay, Dov; Guenthner, Franz (eds.). 444:. In Gabbay, Dov; Guenthner, Franz (eds.). 414: 293:pioneered the structural approach to scope. 1176: 1162: 985: 741:(2 ed.). Wiley Blackwell. Section 5. 640: 436: 184:Haddock description: The rabbit in the hat 988:"Quantifier scope in formal linguistics." 917: 879: 643:"Quantifier scope in formal linguistics." 554:. Cambridge University Press. p. 92. 546: 439:"Quantifier scope in formal linguistics." 95:Every hedgehog is friends with a giraffe. 1079:. Berlin: de Gruyter. pp. 334–356. 1039:. In Lappin, Shalom; Fox, Chris (eds.). 935: 769: 737:. In Lappin, Shalom; Fox, Chris (eds.). 694:. In Lappin, Shalom; Fox, Chris (eds.). 514:. In Lappin, Shalom; Fox, Chris (eds.). 285: 840: 804: 621: 579: 1854: 1107: 1028: 726: 683: 503: 1605:Discourse representation theory (DRT) 1157: 1024: 1022: 913: 911: 679: 677: 476: 160:can be any of those three relatives. 564: 241: 1872:Formal semantics (natural language) 1518:Quantificational variability effect 1185:Formal semantics (natural language) 479:"When even no's Neg is splitsville" 354:and Mats Rooth. This approach uses 120:The company need fire no employees. 13: 1041:Handbook of Contemporary Semantics 1019: 908: 739:Handbook of Contemporary Semantics 696:Handbook of Contemporary Semantics 674: 516:Handbook of Contemporary Semantics 78: 14: 1908: 986:Ruys, Eddy; Winter, Yoad (2011). 641:Ruys, Eddy; Winter, Yoad (2011). 437:Ruys, Eddy; Winter, Yoad (2011). 310:Hypothesis about scope and domain 54:and a single surface form can be 196: 1101: 1065: 995:Handbook of Philosophical Logic 979: 973:Semantics in Generative Grammar 957: 929: 873: 834: 798: 763: 720: 650:Handbook of Philosophical Logic 446:Handbook of Philosophical Logic 424:Semantics in Generative Grammar 316:This view is widely adopted in 1600:Combinatory categorial grammar 634: 615: 573: 558: 540: 497: 470: 430: 408: 224:will you inherit a fortune if 110: 1: 1378:Antecedent-contained deletion 925:. Cambridge University Press. 402: 73: 7: 1003:10.1007/978-94-007-0479-4_3 818:10.1007/978-94-011-3969-4_8 658:10.1007/978-94-007-0479-4_3 454:10.1007/978-94-007-0479-4_3 365: 10: 1913: 1897:Syntax–semantics interface 1259:Syntax–semantics interface 1085:10.1002/9780470758335.ch14 882:Linguistics and Philosophy 859:10.1007/s10988-019-09278-3 847:Linguistics and Philosophy 772:Linguistics and Philosophy 622:Haddock, Nicholas (1987). 589:Linguistics and Philosophy 569:(PhD). Utrecht University. 387:Logical form (linguistics) 372:Continuation-passing style 282:Formal approaches to scope 1788: 1751:Question under discussion 1701:Conversational scoreboard 1678: 1582: 1575: 1478:Intersective modification 1463:Homogeneity (linguistics) 1370: 1279: 1272: 1191: 1049:10.1002/9781118882139.ch2 747:10.1002/9781118882139.ch2 704:10.1002/9781118882139.ch2 601:10.1007/s10988-017-9210-2 524:10.1002/9781118882139.ch2 1806:Distributional semantics 943:. Dordrecht: D. Reidel. 567:The scope of indefinites 392:Quantifier (linguistics) 299:structural view of scope 1801:Computational semantics 1543:Subsective modification 1347:Propositional attitudes 841:Charlow, Simon (2020). 784:10.1023/A:1005349801431 580:Bumford, Dylan (2017). 178:such as the following: 1892:Philosophy of language 1831:Philosophy of language 1473:Inalienable possession 1453:Free choice inferences 1448:Faultless disagreement 1219:Generalized quantifier 483:Jorge Hankamer WebFest 382:Generalized quantifier 294: 257:generalized quantifier 130:existential quantifier 56:semantically ambiguous 1731:Plural quantification 1625:Inquisitive semantics 1590:Alternative semantics 477:Potts, Chris (2000). 289: 263:approach proposed by 164:Definite descriptions 1716:Function application 1523:Responsive predicate 1513:Privative adjectives 1122:. Dordrecht: Foris. 259:denotations. On the 176:Haddock descriptions 1796:Cognitive semantics 1711:Existential closure 1655:Situation semantics 1558:Temperature paradox 1528:Rising declaratives 1493:Modal subordination 1468:Hurford disjunction 1428:Discourse relations 565:Eddy, Ruys (1992). 335:operations such as 48:syntactic positions 41:order of operations 1841:Semantics of logic 1766:Strict conditional 1741:Quantifier raising 1706:Downward entailing 1686:Autonomy of syntax 1615:Generative grammar 1595:Categorial grammar 1533:Scalar implicature 1438:Epistemic modality 1413:De dicto and de re 894:10.1007/BF00351935 810:Events and grammar 377:De dicto and de re 350:first proposed by 348:type shifting view 337:quantifier raising 333:syntactic movement 295: 141:distributive scope 132:scoping below it. 1877:Generative syntax 1849: 1848: 1821:Logic translation 1784: 1783: 1776:Universal grinder 1761:Squiggle operator 1721:Meaning postulate 1660:Supervaluationism 1630:Intensional logic 1610:Dynamic semantics 1571: 1570: 1403:Crossover effects 1352:Tense–aspect–mood 1332:Lexical semantics 1012:978-94-007-0478-7 969:Kratzer, Angelika 950:978-90-277-0778-9 827:978-1-4020-0289-2 806:Kratzer, Angelika 667:978-94-007-0478-7 463:978-94-007-0478-7 420:Kratzer, Angelika 242:Exceptional scope 137:existential scope 1904: 1826:Linguistics wars 1756:Semantic parsing 1645:Montague grammar 1580: 1579: 1423:Deontic modality 1277: 1276: 1264:Truth conditions 1199:Compositionality 1192:Central concepts 1178: 1171: 1164: 1155: 1154: 1149: 1148: 1146: 1140:. 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Retrieved 482: 472: 445: 432: 423: 410: 397:Type shifter 361: 347: 345: 330: 322:logical form 315: 309: 298: 296: 277: 254: 245: 237: 234: 225: 220: 209: 200: 187: 175: 172:infelicitous 162: 157: 153: 150: 140: 136: 134: 123: 114: 104: 100: 98: 88: 82: 60:logical form 45: 28: 24: 18: 1862:Linguistics 1691:Context set 1665:Type theory 1548:Subtrigging 1312:Disjunction 1239:Proposition 965:Heim, Irene 888:(1): 3–44. 416:Heim, Irene 191:witness set 156:dies where 111:Split scope 33:proposition 1856:Categories 1836:Pragmatics 1488:Mirativity 1254:Speech act 1209:Entailment 1204:Denotation 1129:9067652679 403:References 318:generative 168:presuppose 85:word order 1867:Semantics 1640:Mereology 1576:Formalism 1458:Givenness 1383:Cataphora 1371:Phenomena 1362:Vagueness 1292:Ambiguity 1244:Reference 1224:Intension 1214:Extension 867:254749307 609:254742178 489:30 August 326:c-command 212:extracted 74:Phenomena 1789:See also 1679:Concepts 1553:Telicity 1388:Coercion 1342:Negation 1337:Modality 1287:Anaphora 1138:96440512 1111:(1986). 1032:(2015). 971:(1998). 921:(2010). 902:64174420 792:58351641 730:(2015). 687:(2015). 550:(2010). 507:(2015). 422:(1998). 366:See also 37:negation 1887:Grammar 1297:Binding 1034:"Scope" 732:"Scope" 689:"Scope" 509:"Scope" 341:islands 124:On the 31:," the 1882:Syntax 1726:Monads 1273:Topics 1136:  1126:  1091:  1055:  1009:  947:  900:  865:  824:  790:  753:  710:  664:  607:  530:  460:  66:, and 64:monads 23:, the 1418:De se 1322:Focus 1280:Areas 1249:Scope 1145:(PDF) 1134:S2CID 1116:(PDF) 1037:(PDF) 991:(PDF) 898:S2CID 863:S2CID 788:S2CID 735:(PDF) 692:(PDF) 646:(PDF) 605:S2CID 585:(PDF) 512:(PDF) 442:(PDF) 231:dies? 126:de re 25:scope 1124:ISBN 1089:ISBN 1053:ISBN 1007:ISBN 945:ISBN 822:ISBN 751:ISBN 708:ISBN 662:ISBN 528:ISBN 491:2020 458:ISBN 297:The 273:free 139:and 1670:TTR 1081:doi 1045:doi 999:doi 890:doi 855:doi 814:doi 780:doi 743:doi 700:doi 654:doi 597:doi 520:doi 450:doi 43:. 19:In 1858:: 1132:. 1087:. 1051:. 1021:^ 1005:. 967:; 910:^ 896:. 884:. 861:. 851:43 849:. 845:. 820:. 786:. 776:20 774:. 749:. 706:. 676:^ 660:. 626:. 603:. 593:40 591:. 587:. 526:. 481:. 456:. 418:; 343:. 328:. 305:: 70:. 1177:e 1170:t 1163:v 1097:. 1083:: 1061:. 1047:: 1015:. 1001:: 953:. 904:. 892:: 886:1 869:. 857:: 830:. 816:: 794:. 782:: 759:. 745:: 716:. 702:: 670:. 656:: 611:. 599:: 536:. 522:: 493:. 466:. 452:: 228:i 226:t 221:i 158:x 154:x

Index

formal semantics
proposition
negation
order of operations
syntactic positions
surface position
semantically ambiguous
logical form
monads
continuations
word order
de re
existential quantifier
Definite descriptions
presuppose
infelicitous
witness set
extracted
generalized quantifier
choice function
Tanya Reinhart
Angelika Kratzer
free

Tanya Reinhart
Tanya Reinhart
generative
logical form
c-command
syntactic movement

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