Types and Sorts: Resource Logic for Feature Checking

5 I Classification and Composition 7 1 Grammars and Categories 11 1.1 Phrase Structure Grammars . . . . . . . . . . . . . . . . . . . . . 11 1.2 Categorial Grammars . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Multi-modal Categorial Grammars 25 2.1 The Logic of Parts and Wholes . . . . . . . . . . . . . . . . . . . 25 2.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Mixed-Multimodal . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4 Alternative Proof Presentations . . . . . . . . . . . . . . . . . . 40 3 Generalised Phrase Structure Grammars 45 3.1 Feature Structure Theories . . . . . . . . . . . . . . . . . . . . . 45 3.2 Feature Structures and Grammars . . . . . . . . . . . . . . . . . 53 3.2.1 Subsumption-based Grammars . . . . . . . . . . . . . . 54 3.2.2 Unification-based Grammars and Beyond . . . . . . . . 56 3.2.3 Stand-Alone Feature Structure Grammars . . . . . . . . 60 4 Compare and Combine 69 4.1 Global Grammar Architecture . . . . . . . . . . . . . . . . . . . 70 4.2 Comparing the Frameworks . . . . . . . . . . . . . . . . . . . . 72 II Options and Obstacles 87 5 Options for Category Refinement 93 5.1 Bach’s Extended Categorial Grammar . . . . . . . . . . . . . . . 93 5.2 Categorial Unification Grammar . . . . . . . . . . . . . . . . . 96 5.3 Extended Lambek Grammar . . . . . . . . . . . . . . . . . . . . 101 5.4 First-order Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.4.1 AB-Version . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.4.2 Lambek version . . . . . . . . . . . . . . . . . . . . . . . 104 5.5 Fibered Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 105 6 Underspecification in categorial grammars 111 6.1 Unification-based Categorial Grammars . . . . . . . . . . . . . 111 6.2 Type-Logical Grammars . . . . . . . . . . . . . . . . . . . . . . . 114 6.3 Shortcomings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

[1]  Esther König,et al.  LexGram - a practical categorial grammar formalism , 1995, ArXiv.

[2]  Joachim Lambek,et al.  On the Calculus of Syntactic Types , 1961 .

[3]  Mark L. Johnson,et al.  Features and Agreement in Lambek Categorial Grammar , 1995 .

[4]  Petra Hendriks,et al.  Comparatives and Categorial Grammar , 1995 .

[5]  V. M. Abrusci,et al.  Proofs and Linguistic Categories : Applications of Logic to the Analysis and Implementation of Natural Language , 2007 .

[6]  Stuart M. Shieber,et al.  Separating Linguistic Analyses from Linguistic Theories , 1988 .

[7]  Geoffrey K. Pullum,et al.  Generalized Phrase Structure Grammar , 1985 .

[8]  Fernando Pereira,et al.  The Semantics of Grammar Formalisms Seen as Computer Languages , 1984, ACL.

[9]  N. Curteanu.  Book Reviews: Lecture on Contemporary Syntactic Theories: An Introduction to Unification-Based Approaches to Grammar , 1987, CL.

[10]  R. Goldblatt.  Logics of Time and Computation , 1987 .

[11]  Noam Chomsky,et al.  The Minimalist Program , 1992 .

[12]  Bob Carpenter,et al.  Categorial Grammars, Lexical Rules and the English Predicative , 1995 .

[13]  Geoffrey K. Pullum,et al.  Category Structures , 1988, Comput. Linguistics.

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

[15]  Edith Hemaspaandra,et al.  A modal perspective on the computational complexity of attribute value grammar , 1993, J. Log. Lang. Inf..

[16]  Kosta Dosen,et al.  A Brief Survey of Frames for the Lambek Calculus , 1992, Math. Log. Q..

[17]  Dov M. Gabbay,et al.  Fibred semantics for feature-based grammar logic , 1996, J. Log. Lang. Inf..

[18]  Ivan A. Sag,et al.  Information-based syntax and semantics , 1987 .

[19]  Glyn Morrill,et al.  Heads and Phrases. Type Calculus for Dependency and Constituent Structure , 1991 .

[20]  Karen Spärck Jones,et al.  Readings in natural language processing , 1986 .

[21]  Noam Chomsky,et al.  The Sound Pattern of English , 1968 .

[22]  Stuart M. Shieber,et al.  Constraint-based grammar formalisms , 1992 .

[23]  Reinhard Muskens,et al.  Categorial Grammar and Discourse Representation Theory , 1994, COLING.

[24]  Yehoshua Bar-Hillel,et al.  Language and Information , 1964 .

[25]  Nissim Francez.  On the direction of fibring feature logics with concatenation logics , 1997 .

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

[27]  E. Bach,et al.  An extension of classical transformational gram-mar , 1976 .

[28]  Martin Kay,et al.  Parsing in functional unification grammar , 1986 .

[29]  Geoffrey K. Pullum,et al.  Phonological Resolution of Syntactic Feature Conflict , 1986 .

[30]  G. Corbett.  8. Resolution rules: agreement in person, number, and gender , 1983 .

[31]  Gertjan van Noord,et al.  Adjuncts and the Processing of Lexical Rules , 1994, COLING.

[32]  Stephen G. Pulman,et al.  A Computational Framework for Lexical Description , 1987, Comput. Linguistics.

[33]  Marc Moens,et al.  Expressing generalizations in unification-based grammar formalisms , 1989, EACL.

[34]  Mike Reape,et al.  A formal theory of word order : a case study in West Germanic , 1994 .

[35]  IVAN A. SAG, GERALD GAZDAR, THOMAS WASOW, AND STEVEN WEISLER COORDINATION AND HOW TO DISTINGUISH , .

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

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

[38]  Alain Lecomte,et al.  Multimodal Logic for Syntax , 1998 .

[39]  Mark Hepple,et al.  The grammar and processing of order and dependency : a categorial approach , 1990 .

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

[41]  Glyn MorrillCentre,et al.  Grammar and Logical Types , 1990 .

[42]  Martin Kay,et al.  Functional Unification Grammar: A Formalism for Machine Translation , 1984, ACL.

[43]  Sam Bayer,et al.  The Coordination of Unlike Categories. , 1996 .

[44]  Mark Johnson,et al.  Features and Agreement , 1995, ACL.

[45]  R. Borsley.  Syntactic Theory: A Unified Approach , 1991 .

[46]  Patrick Blackburn,et al.  Decidability and Undecidability in stand-alone Feature Logics , 1993, EACL.

[47]  Patrick Blackburn.  Structures, Languages and Translations: the Structural Approach to Feature Logic , 1994 .

[48]  Jochen Dörre,et al.  Feature Logic with Weak Subsumption Constraints , 1991, ACL.

[49]  Gerald Gazdar,et al.  Inference in DATR , 1989, EACL.

[50]  Reinhard Muskens,et al.  Talking about Trees and Truth-Conditions , 2001, J. Log. Lang. Inf..

[51]  Makoto Kanazawa.  The Lambek calculus enriched with additional connectives , 1992, J. Log. Lang. Inf..

[52]  William C. Rounds,et al.  Feature Logics , 1997, Handbook of Logic and Language.

[53]  D. Prawitz.  Natural Deduction: A Proof-Theoretical Study , 1965 .

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

[55]  Joachim Lambek,et al.  Type Grammar Revisited , 1997, LACL.

[56]  Kees van Deemter,et al.  Semantic ambiguity and underspecification , 1996 .

[57]  Wojciech Buszkowski,et al.  Mathematical Linguistics and Proof Theory , 1997, Handbook of Logic and Language.

[58]  Emmon Bach,et al.  On the relationship between word-grammar and phrase-grammar , 1983 .

[59]  W. Buszkowski.  Generative Power of Categorial Grammars , 1988 .

[60]  Mark Johnson,et al.  Attribute-value logic and the theory of grammar , 1988 .

[61]  Mark Johnson,et al.  A Resource Sensitive Interpretation of Lexical Functional Grammar , 1999, J. Log. Lang. Inf..

[62]  Robert Ingria,et al.  The Limits of Unification , 1990, ACL.

[63]  N. Kurtonina,et al.  Frames and Labels , 1995 .

[64]  Bob Carpenter,et al.  The logic of typed feature structures , 1992 .

[65]  Claire Gardent,et al.  Talking About Trees , 1993, EACL.

[66]  Eric Bach,et al.  Generalized Categorial Grammars and the English Auxiliary , 1983 .

[67]  M. Andrew Moshier,et al.  Featureless HPSG , 1997 .

[68]  Jochen Dörre,et al.  On Constraint-Based Lambek Calculi , 1995, ArXiv.

[69]  P. Blackburn.  Modal Logic and Attribute Value Structures , 1993 .

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

[71]  M. Moortgat,et al.  Structural Abstractions , 1996 .

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

[73]  H. B. Allen,et al.  A Functional Grammar , 1946 .

[74]  Ewan Klein,et al.  Type-driven translation , 1985 .