Covert Movement in Logical Grammar

We propose a formal reconstruction of the well-known storage-and-retrieval technique for scoping quantifiers and other 'covertly moved' semantic operators due to Cooper (1975). In the proposed reconstruction, grammar rules are presented in the familiar term-labelled Gentzensequent style of natural deduction.What is new is that, in addition to the usual contexts to the left of the turnstile (recording undischarged pairs of hypotheses, with each pair consisting of a syntactic variable ('trace') and a corresponding semantic variable), our typing judgments also include a co-context to the right of the co-turnstile (⊣). A co-context consists of a list of semantic variables, each paired with a quantifier that corresponds to the meaning expressed by a quantified noun phrase whose scope has not yet been specified. Besides the usual logical rules, the grammar also contains rules called Commitment and Responsibility that implement, respectively, storage and retrieval of semantic operators.

[1]  Michel Parigot,et al.  Lambda-Mu-Calculus: An Algorithmic Interpretation of Classical Natural Deduction , 1992, LPAR.

[2]  David Pearce,et al.  Nonclassical Logics and Information Processing , 1992, Lecture Notes in Computer Science.

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

[4]  Daniel Gallin,et al.  Intensional and Higher-Order Modal Logic , 1975 .

[5]  J. Roger Hindley,et al.  To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism , 1980 .

[6]  Carl Pollard,et al.  Hyperintensional Questions , 2008, WoLLIC.

[7]  Matthias Felleisen,et al.  The theory and practice of first-class prompts , 1988, POPL '88.

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

[9]  W. Buszkowski.  The Logic of Types , 1987 .

[10]  Michael Moortgat,et al.  Categorial Type Logics , 1997, Handbook of Logic and Language.

[11]  J. Lambek,et al.  Categorial and Categorical Grammars , 1988 .

[12]  William C. Frederick,et al.  A Combinatory Logic , 1995 .

[13]  Michael Moortgat,et al.  Continuation Semantics for Symmetric Categorial Grammar , 2007, WoLLIC.

[14]  C. Barry Jay,et al.  Languages for monoidal categories , 1989 .

[15]  Dov M. Gabbay,et al.  Extending the Curry-Howard interpretation to linear, relevant and other resource logics , 1992, Journal of Symbolic Logic.

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

[17]  Alice G. B. ter Meulen,et al.  The representation of (in)definiteness , 1989 .

[18]  Robin Cooper,et al.  The syntax and semantics of when-questions , 1982 .

[19]  Pauline Jacobson.  Towards a Variable-Free Semantics , 1999 .

[20]  G. Mints,et al.  Closed categories and the theory of proofs , 1981 .

[21]  Johan van Benthem,et al.  Handbook of Logic and Language , 1996 .

[22]  Aarne Ranta,et al.  Grammatical Framework , 2004, Journal of Functional Programming.

[23]  Johan van Benthem,et al.  The semantics of variety in categorial grammar , 1988 .

[24]  Noam Chomsky,et al.  On Wh-Movement , 1977 .

[25]  Glyn Morrill,et al.  Type Logical Grammar: Categorial Logic of Signs , 1994 .

[26]  C. Barker.  Continuations and the Nature of Quantification , 2002 .

[27]  Robin Hayes Cooper,et al.  MONTAGUE'S SEMANTIC THEORY AND TRANSFORMATIONAL SYNTAX. , 1975 .

[28]  Noam Chomsky,et al.  Lectures on Government and Binding , 1981 .

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

[30]  J. Srzednicki,et al.  Initiatives in Logic , 2011 .

[31]  J. Lambek.  The Mathematics of Sentence Structure , 1958 .

[32]  Cheng-Teh James Huang,et al.  Logical Relations in Chinese and the Theory of Grammar , 1998 .

[33]  Michel Parigot,et al.  On the Computational Interpretation of Negation , 2000, CSL.

[34]  Frank Pfenning,et al.  Logic Programming and Automated Reasoning , 1994, Lecture Notes in Computer Science.

[35]  Bi-grammars : a logical system for syntax , semantics and their correspondence , .

[36]  M. Moortgat.  Generalized quantifiers and discontinuous type constructors , 1996 .

[37]  Alan Bundy,et al.  Towards Ontology Evolution in Physics , 2008, WoLLIC.

[38]  Emmon W. Bach,et al.  Categorial Grammars and Natural Language Structures , 1988 .

[39]  Martin Stokhof,et al.  Proceedings of the Thirteenth Amsterdam Colloquium , 2001 .

[40]  Barbara H. Partee,et al.  Anaphora and Semantic Structure , 2008 .

[41]  C. Pollard.  The calculus of responsibility and commitment , 2011 .

[42]  C. Barker.  Parasitic scope , 2007 .

[43]  Mark Steedman,et al.  Surface structure and interpretation , 1996, Linguistic inquiry.

[44]  Michael Moortgat,et al.  Symmetries in Natural Language Syntax and Semantics: The Lambek-Grishin Calculus , 2007, WoLLIC.

[45]  Reinhard Muskens,et al.  Language, Lambdas, and Logic , 2003 .

[46]  R. Montague.  Formal philosophy; selected papers of Richard Montague , 1974 .

[47]  William A. Howard,et al.  The formulae-as-types notion of construction , 1969 .

[48]  Gerald Gazdar,et al.  Unbounded Dependencies and Coordinate Structure , 1981 .

[49]  Joseph E. Aoun.  'Wh'- elements in situ: syntax or lF? , 1993 .

[50]  Ian Mackie,et al.  An internal language for autonomous categories , 1993, Theory and Formal Methods.

[51]  Mark Ryan,et al.  Proceedings of the First Imperial College Department of Computing Workshop on Theory and formal methods 1993 , 1993, FME 1993.

[52]  R. May.  The grammar of quantification , 1978 .

[53]  Alain Lecomte,et al.  Linear Grammars with Labels , 2006 .

[54]  Sylvain Pogodalla,et al.  About Parallel and Syntactocentric Formalisms: A Perspective from the Encoding of Convergent Grammar into Abstract Categorial Grammar , 2011, Fundam. Informaticae.

[55]  J. Zwart.  The Minimalist Program , 1998, Journal of Linguistics.

[56]  M. Moortgat.  Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus , 1988 .

[57]  Olivier Danvy,et al.  Abstracting control , 1990, LISP and Functional Programming.

[58]  Chung-chieh Shan,et al.  A continuation semantics of interrogatives that accounts for Baker's ambiguity , 2002, ArXiv.

[59]  Heinrich Wansing,et al.  Formulas-as-types for a Hierarchy of Sublogics of Intuitionistic Propositional Logic , 1992, Nonclassical Logics and Information Processing.

[60]  Claudia Faggian,et al.  Institut de Mathématiques de Luminy , 2004 .

[61]  Richard T. Oehrle,et al.  Term-labeled categorial type systems , 1994 .

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

[63]  Jaakko Hintikka,et al.  Approaches to natural language : proceedings of the 1970 Stanford workshop on grammar and semantics , 1973 .

[64]  Jeroen Groenendijk,et al.  On the semantics of questions and the pragmatics of answers , 1984 .

[65]  Reinhard Muskens,et al.  Type-logical semantics , 2010 .

[66]  Valeria C V de Paiva,et al.  Term Assignment for Intuitionistic Linear Logic , 1992 .

[67]  Chung-chieh Shan,et al.  Delimited continuations in natural language: quantification and polarity sensitivity , 2004, ArXiv.

[68]  Philippe de Groote,et al.  Towards Abstract Categorial Grammars , 2001, ACL.

[69]  Nick Benton,et al.  A Term Calculus for Intuitionistic Linear Logic , 1993, TLCA.

[70]  H.L.W. Hendriks,et al.  Studied flexibility : categories and types in syntax and semantics , 1993 .

[71]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[72]  Hugo Herbelin,et al.  The duality of computation , 2000, ICFP '00.