Categorial Minimalist Grammar

We first recall some basic notions on minimalist grammars and on categorial grammars. Next we shortly introduce partially commutative linear logic, and our representation of minimalist grammars within this categorial system, the so-called categorial minimalist grammars. Thereafter we briefly present \lambda\mu-DRT (Discourse Representation Theory) an extension of \lambda-DRT (compositional DRT) in the framework of \lambda\mu calculus: it avoids type raising and derives different readings from a single semantic representation, in a setting which follows discourse structure. We run a complete example which illustrates the various structures and rules that are needed to derive a semantic representation from the categorial view of a transformational syntactic analysis.

[1]  Sylvain Salvati,et al.  Minimalist Grammars in the Light of Logic , 2011, Logic and Grammar.

[2]  C. Retoré,et al.  Natural Deduction and Normalisation for Partially Commutative Linear Logic and Lambek Calculus with Product , 2007 .

[3]  Samson Abramsky,et al.  Computational Interpretations of Linear Logic , 1993, Theor. Comput. Sci..

[4]  Jens Michaelis,et al.  Transforming Linear Context-Free Rewriting Systems into Minimalist Grammars , 2001, LACL.

[5]  P. D. Groote,et al.  Partially commutative linear logic: sequent calculus and phase semantics , 1996 .

[6]  Gregory M. Kobele,et al.  An Automata-Theoretic Approach to Minimalism , 2007 .

[7]  M. Baratin,et al.  L'Analyse linguistique dans l'antiquité classique , 1981 .

[8]  Noam Chomsky.  A minimalist program for linguistic theory , 1992 .

[9]  Los Angeles,et al.  Generating Copies: An investigation into structural identity in language and grammar , 2006 .

[10]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[11]  Jens Michaelis,et al.  Derivational Minimalism Is Mildly Context-Sensitive , 1998, LACL.

[12]  Tom Cornell,et al.  Derivational and Representational Views of Minimalist Tranformational Grammar , 1997, LACL.

[13]  Christian Retoré,et al.  Extending Lambek Grammars: a Logical Account of Minimalist Grammars , 2001, ACL.

[14]  Jens Michaelis,et al.  Derivational minimalism in two regular and logical steps , 2000, TAG+.

[15]  C. Retoré,et al.  Learning Rigid Lambek Grammars and Minimalist Grammars from Structured Sentences ? , 2001 .

[16]  Y. Bar-Hillel.  A Quasi-Arithmetical Notation for Syntactic Description , 1953 .

[17]  Christian Retoré,et al.  Towards a minimal logic for minimalist grammars: a trans-formational use of Lambek calculus , 1999 .

[18]  Edward P. Stabler,et al.  Derivational Minimalism , 1996, LACL.

[19]  Edward P. Stabler,et al.  Generative Grammars in Resource Logics , 2004 .

[20]  M. Brody.  Lexico-Logical Form: A Radically Minimalist Theory , 1995 .

[21]  Alain Lecomte.  Semantics in Minimalist Categorial Grammar , 2008 .

[22]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[23]  Maxime Amblard,et al.  Syntax and Semantics interacting in a Minimalist theory , 2004 .

[24]  Maxime Amblard,et al.  Calculs de représentations sémantiques et syntaxe générative : les grammaires minimalistes catégorielles. (Sémantic representations and generative grammar: the Minimalist Categorial Grammars) , 2007 .

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

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

[27]  Willemijn Vermaat.  The Minimalist Move Operation in a Deductive Perspective , 2004 .

[28]  Houda Anoun,et al.  Approche logique des grammaires pour les langues naturelles. (A logical approach to grammar for natural languages) , 2007 .