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Quantifier Scope, Lexical Semantics, and Surface Structure Constituency University of Pennsylvania ScholarlyCommons IRCS Technical Reports Series Institute for Research in Cognitive Science December 1996 Quantifier Scope, Lexical Semantics, and Surface Structure Constituency Jong Cheol Park University of Pennsylvania Follow this and additional works at: https://repository.upenn.edu/ircs_reports Park, Jong Cheol, "Quantifier Scope, Lexical Semantics, and Surface Structure Constituency" (1996). IRCS Technical Reports Series. 106. https://repository.upenn.edu/ircs_reports/106 University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-96-28. This paper is posted at ScholarlyCommons. https://repository.upenn.edu/ircs_reports/106 For more information, please contact [email protected]. Quantifier Scope, Lexical Semantics, and Surface Structure Constituency Abstract We present a novel conjecture concerning the scope ambiguities that arise in sentences including multiple nonreferential quantifiers. eW claim that many existing theories of the phenomenon fail to correctly limit the set of readings that such sentences engender by failing to distinguish between referential and non-referential quantifiers. Once the distinction is correctly drawn, we show that surface syntax can be made, via an extended notion of surface constituency, to identify the set of available differently-scoped readings for such sentences. We examine various English constructions to show that the scopings predicted by the conjecture are the only ones that are available to human language understanders. We show how to incorporate this conjecture into a theory of quantifier scope, yb couching it in a unification-based Combinatory Categorial Grammar framework and implementing it in SICStus Prolog. Finally, we compare the proposal with related approaches to quantifier scope ambiguity. Comments University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-96-28. This technical report is available at ScholarlyCommons: https://repository.upenn.edu/ircs_reports/106 , Institute for Research in Cognitive Science Quantifier Scope, Lexical Seman- tics, and Surface Structure Constituency Jong Cheol Park University of Pennsylvania 3401 Walnut Street, Suite 400A Philadelphia, PA 19104-6228 December 1996 Site of the NSF Science and Technology Center for Research in Cognitive Science IRCS Report 96--28 Quantier Scop e Lexical Semantics and Surface Structure Constituency Jong C Park UniversityofPennsylvania We present a novel conjectureconcerning the scope ambiguities that arise in sentences including multiple nonreferential quantiers We claim that many existing theories of the phenomenon fail to correctly limit the set of readings that such sentences engender by failing to distinguish between referential and nonreferential quantiers Once the dis tinction is correctly drawn we show that surfacesyntaxcan be made via an extended notion of surfaceconstituency to identify the set of available dierentlyscopedreadings for such sentences We examine various English constructions to show that the scop ings predicted by the conjectureare the only ones that are available to human language understanders We show how to incorporate this conjecture into a theory of quantier scope by couching it in a unicationbased Combinatory Categorial Grammar framework and implementing it in SICStus Prolog Final ly we compare the proposal with related approaches to quantier scope ambiguity Intro duction The semantics of sentences containing quantiers can b e dicult to predict Particularly when a sentence contains multiple quantiers the scop e p ossibilities for each quantier mayinteract in unexp ected ways with each other and with other syntactic prop erties of the sentence Many theories of quantier scop e have b een prop osed in the literature most of them variants either of quantier raising as prop osed byMay or of quantifying in as prop osed byMontague Both prop osals op erate under the assumption that the semantics of quantiers can b e characterized by abstraction according to whichNP semantics can b e pulled out of the original NP p osition and take the rest of the sentential semantics or some part thereof under its scop e According to these prop osals whether two NPs mayormay not alternate their relative scop e order can only b e determined after the two NPs are individually abstracted out Despite numerous mo dications of these original prop osals they still app ear to fall short of explanatory and descriptive adequacy for reasons that are discussed in Section b elow In this pap er we presentanovel conjecture that predicts when two nonreferential quantiers are or are not ambiguous with resp ect to their relative scop e This approach ties scop e ambiguity in a language to co ordination in the language Which substrings serve as scop e islands can b e predicted from which substrings can b e co ordinated We claim that the conjecture makes predictions that are b oth explanatory and descriptively adequate To substantiate this claim this pap er fo cuses on three kinds of English con structions that allowmultiple NPs in a single grammatical sentence complex NPs con Department of Computer and Information Science UniversityofPennsylvania Philadelphia PA Email parklinccisupennedu A preliminary sketch app ears in Park Jong Park A Lexical Theory of Quantier Scop e taining PPs complex NPs containing Whrelatives and transitiveattitude verbs We also give a theory of quantier scop e that is couched in Combinatory Categorial Gram mar CCG formalism and implemented in SICStus Prolog The pap er is structured as follows Section motivates and lays out the conjecture for scop e ambiguity Section argues whywe need to distinguish referential NP inter pretations from quanticational NP interpretations in semantics following Fo dor and Sag Section presents a comp etence theory of quantier scop e couched in a unicationbased CCG framework While CCG is chosen for this task since its notion of constituency meshes well with that assumed in the conjecture it should also b e p ossi ble to sp ell out the theory in other grammar formalisms Section lays out theoretical predictions on scop e readings Section compares the presentapproach with traditional approaches to quantier scop e Complete prolog co de for the example sentences consid ered in this pap er and some sample runs are given in an app endix Surface Constituency Conjecture Consider the following sentences a Every representative of a companysaw most samples b Some studentwillinvestigate two dialects of every language Hobbs and Shieb er made a claim based on quantier binding at LF that out of the six combinatorial ways of ordering the three quantiers ie every a and most sentence a has one missing scop e reading in which every representative outscop es most sampleswhic h in turn outscop es acompany This scop e reading is certainly unavailable from sentence a Notice that in this claim Hobbs Shieb er implicitly assumed that among the available ve readings is the one in which acompany outscop es most sampleswhich in turn outscop es every representative Let us call this Hobbs Shieb ers reading The reading would b e true of a situation in which there is a company such that most samples were individually seen bytheentire representatives of that particular companyWe agree that Hobbs Shieb ers reading is available from sentence a May claimed that sentence b has a reading in which every language outscop es some student which in turn outscop es two dialects Let us call this Mays reading This reading would b e true of a situation in which for each language there is a p ossibly dierent studentsuch that he or she will investigate two dialects of that language Again we agree that Mays reading is available from sentence b Notice that these two readings share an interesting pattern where the two NPs NP prep NP andNP ignoring the word order give rise to a scop e order in whichNP outscop es NP whichin turn outscop es NP This pattern suggests that standard English constituent structure or even the extended notion of surface constituency discussed b elow do es not limit the range of available readings Nevertheless weshow in Section that the kind of scop e relation implicated in Hobbs Shieb ers account of their reading is unavailable for quanticational NPs eg at least two companies or few companies in place of acompany This is due to the kind of functional dep endency inherentinquanticational scop e relations to b e discussed later There is an inherent realworld connection b etween languages and dialects This connection app ears to interfere with the said scop e relation in suchaway that mightoverride an otherwise unavailable scop e relation This p otential interference would go awayifwe replace two dialects with two aspects Bonnie Webb er and TonyKroch pc The change makes the fact clearer that the said scop e reading is available indep endentofsucharealworld connection Jong Park A Lexical Theory of Quantier Scop e The reason Hobbs Shieb ers reading is available for sentence a is we b elieve that acompany can b e interpreted referentially Heim We know following Fo dor and Sag that while referential NPs app ear to take matrix scop e they do not really participate in the kind of scop e relations that quanticational NPs do Most crucially referential NPs are interpreted relatively indep endently of the rest of the NPs in the same sentence and the rest of the NPs are interpreted as if referential NPs are more or less prop er nouns It is thus theoretically
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