Dependency Tree Semantics

This paper presents Dependency Tree Semantics (DTS), an underspecified logic for representing quantifier scope ambiguities. DTS features a direct interface with a Dependency grammar, an easy management of partial disambiguations and the ability to represent branching quantifier readings. This paper focuses on the syntax of DTS, while does not take into account the model-theoretic interpretation of its well-formed structures.

[1]  Joachim Niehren,et al.  The Constraint Language for Lambda Structures , 2001, J. Log. Lang. Inf..

[2]  Gert Smolka,et al.  A Relational Syntax-Semantics Interface Based on Dependency Grammar , 2004, COLING.

[3]  Perlindström First Order Predicate Logic with Generalized Quantifiers , 1966 .

[4]  J. Benthem Essays in Logical Semantics , 1986 .

[5]  Maryellen C. MacDonald,et al.  Resolution of quantifier scope ambiguities , 1993, Cognition.

[6]  Johan Bos,et al.  Computational Semantics in Discourse: Underspecification, Resolution, and Inference , 2004, J. Log. Lang. Inf..

[7]  Uli Sauerland,et al.  Cumulation is needed: A reply to Winter , 2000 .

[8]  Jerry R. Hobbs,et al.  An Algorithm for Generating Quantifier Scopings , 1987, CL.

[9]  Mary Dalrymple,et al.  Lexical Functional Grammar , 2001 .

[10]  Mark Steedman,et al.  A lexical theory of quantification in ambiguous query interpretation , 1996 .

[11]  R. Scha Distributive, Collective and Cumulative Quantification , 1984 .

[12]  Aravind K. Joshi,et al.  Tree-Adjoining Grammars , 1997, Handbook of Formal Languages.

[13]  A. Joshi,et al.  Factoring Predicate Argument and Scope Semantics: Underspecified Semantics with LTAG , 2003 .

[14]  David R. Dowty,et al.  Introduction to Montague semantics , 1980 .

[15]  Uwe Reyle,et al.  Co-Indexing Labelled DRSs to Represent and Reason with Ambiguities , 1995, ArXiv.

[16]  Elisabeth Villalta,et al.  The Role of Context in the Resolution of Quantifier Scope Ambiguities , 2003, J. Semant..

[17]  Johan Bos,et al.  Predicate logic unplugged , 1996 .

[18]  Richard K. Larson,et al.  Quantifying into NP * , 2002 .

[19]  Stanley Peters,et al.  Quantifiers in language and logic , 2006 .

[20]  Fred Landman,et al.  Events and Plurality: The Jerusalem Lectures , 2001 .

[21]  Pasi Tapanainen Parsing in two frameworks: finite-state and functional dependency grammar , 1999 .

[22]  Cristina Bosco,et al.  A GRAMMATICAL RELATION SYSTEM FOR TREEBANK ANNOTATION , 2003 .

[23]  Igor Mel’čuk,et al.  Actants in semantics and syntax II: actants in syntax , 2004 .

[24]  Gila Sher Partially-Ordered (Branching) Generalized Quantifiers: A General Definition , 1997, J. Philos. Log..

[25]  Jaakko Hintikka,et al.  Quantifiers vs. Quantification Theory , 1973 .

[26]  Joachim Niehren,et al.  Bridging the gap between underspecification formalisms: hole semantics as dominance constraints , 2002 .

[27]  Christian Ebert,et al.  Formal investigations of underspecified representations , 2005 .

[28]  Joachim Niehren,et al.  Minimal Recursion Semantics as Dominance Constraints: Translation, Evaluation, and Analysis , 2004, ACL.

[29]  B. Carpenter,et al.  Type-Logical Semantics , 1997 .

[30]  Laura Kallmeyer,et al.  Scope and Situation Binding in LTAG Using Semantic Unification , 2008 .

[31]  Ways of Branching Quantifiers , 2022 .

[32]  Rui P. Chaves Non-redundant scope disambiguation in Underspecified Semantics , 2003 .

[33]  Harry Bunt,et al.  Underspecification in Semantic Representations : Which Technique for What Purpose? , 2003 .

[34]  Irene Heim,et al.  The semantics of definite and indefinite noun phrases : a dissertation , 1982 .

[35]  Peter Aczel Quantifiers; Games and Inductive Definitions , 1975 .

[36]  Vincenzo Lombardo,et al.  Transformed Subcategorization Frames in Chunk Parsing , 2002, LREC.

[37]  Jeroen Groenendijk,et al.  Dynamic predicate logic , 1991 .

[38]  A. Mostowski On a generalization of quantifiers , 1957 .

[39]  Anna Szabolcsi,et al.  Variation, Distributivity, and the Illusion of Branching , 1997 .

[40]  Ivan A. Sag,et al.  Book Reviews: Head-driven Phrase Structure Grammar and German in Head-driven Phrase-structure Grammar , 1996, CL.

[41]  J. van der Does,et al.  The Semantics of Plural Noun Phrases , 1996 .

[42]  Annabel Cormack,et al.  Ambiguity and quantification , 1981 .

[43]  Angelika Kratzer,et al.  On the Plurality of Verbs , 2008 .

[44]  H. Alshawi,et al.  The Core Language Engine , 1994 .

[45]  Wolfgang Sternefeld,et al.  Reciprocity and Cumulative Predication , 1998 .

[46]  William R. Keller,et al.  Nested Cooper Storage: The Proper Treatment of Quantification in Ordinary Noun Phrases , 1988 .

[47]  Ralph Debusmann,et al.  Extensible Dependency Grammar: A New Methodology , 2004, Workshop On Recent Advances In Dependency Grammar.

[48]  J. Gerbrandy,et al.  Quantifiers in Dependency Tree Semantics , 2006 .

[49]  Iddo Lev Decoupling Scope Resolution from Semantic Composition , 2004 .

[50]  Espen J. Vestre An Algorithm For Generating Non-Redundant Quantifier Scopings , 1991, EACL.

[51]  G. Sher Ways of branching quantifers , 1990 .

[52]  Lucien Tesnière Éléments de syntaxe structurale , 1959 .

[53]  Laura Kallmeyer,et al.  Flexible Composition In Ltag: Quantifier Scope and Inverse Linking , 2008 .

[54]  J. Barwise,et al.  Generalized quantifiers and natural language , 1981 .

[55]  David J. Weir,et al.  Characterizing mildly context-sensitive grammar formalisms , 1988 .

[56]  Uli Sauerland,et al.  Cumulation is Needed: A Reply to Winter (2000) , 2000 .

[57]  Gilbert Harman,et al.  Logical Form in Natural Language. , 1986 .

[58]  Dan Flickinger,et al.  Minimal Recursion Semantics: An Introduction , 2005 .

[59]  Uwe Reyle,et al.  Dealing with Ambiguities by Underspecification: Construction, Representation and Deduction , 1993, J. Semant..

[60]  I. I. N. Kamp Combining Montague Semantics and Discourse Representation , 1996 .

[61]  Douglas B. Moran,et al.  Quantifier Scoping in the SRI Core Language Engine , 1988, ACL.

[62]  Kurt Mehlhorn,et al.  A Polynomial-Time Fragment of Dominance Constraints , 2000, ACL.

[63]  Robert May,et al.  Interpreting logical form , 1989 .

[64]  B. Partee Compositionality in formal semantics : selected papers , 2004 .

[65]  Uwe Reyle,et al.  From discourse to logic , 1993 .

[66]  Igor Mel’čuk,et al.  Dependency Syntax: Theory and Practice , 1987 .

[67]  Mary Dalrymple,et al.  A Deductive Account of Quantification in LFG , 1994, ArXiv.

[68]  R. May Logical Form: Its Structure and Derivation , 1985 .

[69]  Cristina Bosco,et al.  Treebank Development: the TUT Approach , 2002 .

[70]  Gilad Ben-Avi,et al.  Monotonicity and Collective Quantification , 2003, J. Log. Lang. Inf..

[71]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[72]  Richard Montague,et al.  The Proper Treatment of Quantification in Ordinary English , 1973 .

[73]  Manfred Krifka,et al.  Thematic Relations as Links between Nominal Reference and Temporal Constitution , 1992 .

[74]  B. Schein Plurals and Events , 1994 .

[75]  Richard Hudson,et al.  English word grammar , 1995 .

[76]  Uwe Reyle,et al.  Principle Based Semantics for HPSG , 1994, EACL.

[77]  Igor Mel,et al.  Semantics and the Lexicon in Modern Linguistics , 2000 .

[78]  Ralph Debusmann,et al.  Extensible dependency grammar: a modular grammar formalism based on multigraph description , 2006 .

[79]  Uwe Reyle,et al.  From Discourse to Logic - Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory , 1993, Studies in linguistics and philosophy.

[80]  Hiyan Alshawi,et al.  Monotonic Semantic Interpretation , 1992, ACL.

[81]  Nirit Kadmon,et al.  On unique and non-unique reference and asymmetric quantification , 1987 .

[82]  K. Jon Barwise,et al.  On branching quantifiers in English , 1979, J. Philos. Log..

[83]  Rui Pedro Chaves,et al.  DRT and Underspecification of Plural Ambiguities ∗ , 2005 .

[84]  Vilmos Ágel,et al.  The Meaning-Text Theory , 2003 .

[85]  Robin Cooper,et al.  Quantification and Syntactic Theory , 1983 .