Incremental Monoidal Grammars

In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model.

[1]  Emil L. Post.  Recursive Unsolvability of a problem of Thue , 1947, Journal of Symbolic Logic.

[2]  Alexandra Silva,et al.  Generalizing determinization from automata to coalgebras , 2013, Log. Methods Comput. Sci..

[3]  Alaa A. Kharbouch,et al.  Three models for the description of language , 1956, IRE Trans. Inf. Theory.

[4]  Wojciech Buszkowski,et al.  Pregroup Grammars and Context-free Grammars , 2007 .

[5]  Mehrnoosh Sadrzadeh,et al.  Experimental Support for a Categorical Compositional Distributional Model of Meaning , 2011, EMNLP.

[6]  Dimitri Kartsaklis,et al.  Separating Disambiguation from Composition in Distributional Semantics , 2013, CoNLL.

[7]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[8]  Stuart M. Shieber,et al.  Evidence against the context-freeness of natural language , 1985 .

[9]  Steve Awodey,et al.  Category Theory , 2006 .

[10]  P. Selinger.  A Survey of Graphical Languages for Monoidal Categories , 2009, 0908.3347.

[11]  Yoshua Bengio,et al.  A Neural Probabilistic Language Model , 2003, J. Mach. Learn. Res..

[12]  S. Kleene.  Review: Emil L. Post, Recursive Unsolvability of a Problem of Thue , 1947 .

[13]  A. Joyal,et al.  The geometry of tensor calculus, I , 1991 .

[14]  James F. Power,et al.  Thue's 1914 paper: a translation , 2013, ArXiv.

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

[16]  Joachim Lambek,et al.  Type Grammars as Pregroups , 2001, Grammars.

[17]  S. Lane.  Categories for the Working Mathematician , 1971 .

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

[19]  Mehrnoosh Sadrzadeh,et al.  Lambek vs. Lambek: Functorial vector space semantics and string diagrams for Lambek calculus , 2013, Ann. Pure Appl. Log..

[20]  Dimitri Kartsaklis,et al.  A Unified Sentence Space for Categorical Distributional-Compositional Semantics: Theory and Experiments , 2012, COLING.

[21]  David J. Weir,et al.  The equivalence of four extensions of context-free grammars , 1994, Mathematical systems theory.

[22]  Stephen Clark,et al.  Mathematical Foundations for a Compositional Distributional Model of Meaning , 2010, ArXiv.

[23]  S. Clark,et al.  A Compositional Distributional Model of Meaning , 2008 .

[24]  Noam Chomsky,et al.  वाक्यविन्यास का सैद्धान्तिक पक्ष = Aspects of the theory of syntax , 1965 .

[25]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[26]  Mehrnoosh Sadrzadeh,et al.  Exploring Semantic Incrementality with Dynamic Syntax and Vector Space Semantics , 2018, ArXiv.