A Frobenius Model of Information Structure in Categorical Compositional Distributional Semantics

The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The theoretical framework allows for reasoning about compositional aspects of language and offers structural ways of studying the underlying relationships. While the model so far has been applied on the level of syntactic structures, a sentence can bring extra information conveyed in utterances via intonational means. In the current paper we extend the framework in order to accommodate this additional information, using Frobenius algebraic structures canonically induced over the basis of finite-dimensional vector spaces. We detail the theory, provide truth-theoretic and distributional semantics for meanings of intonationally-marked utterances, and present justifications and extensive examples.

[1]  Stephen Clark,et al.  The Frobenius anatomy of word meanings I: subject and object relative pronouns , 2013, J. Log. Comput..

[2]  Mirella Lapata,et al.  Vector-based Models of Semantic Composition , 2008, ACL.

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

[4]  Zellig S. Harris,et al.  Mathematical structures of language , 1968, Interscience tracts in pure and applied mathematics.

[5]  Katharina Hartmann,et al.  Subject focus in West African languages , 2010 .

[6]  Martin Kay,et al.  Syntactic Process , 1979, ACL.

[7]  Dimitri Kartsaklis,et al.  Open System Categorical Quantum Semantics in Natural Language Processing , 2015, CALCO.

[8]  Mark Steedman,et al.  Combined Distributional and Logical Semantics , 2013, TACL.

[9]  Hinrich Schütze,et al.  Automatic Word Sense Discrimination , 1998, Comput. Linguistics.

[10]  W. Chafe.  Givenness, contrastiveness, definiteness, subjects, topics, and point of view , 1976 .

[11]  Dimitri Kartsaklis,et al.  Compositional distributional semantics with compact closed categories and Frobenius algebras , 2015, ArXiv.

[12]  Richard Montague,et al.  ENGLISH AS A FORMAL LANGUAGE , 1975 .

[13]  Christopher D. Manning,et al.  Introduction to Information Retrieval , 2010, J. Assoc. Inf. Sci. Technol..

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

[15]  Caroline Féry,et al.  Information structure: Notional distinctions, ways of expression , 2008 .

[16]  G. M. Kelly.  Many-variable functorial calculus. I. , 1972 .

[17]  Mats Rooth.  A theory of focus interpretation , 1992, Natural Language Semantics.

[18]  Patrick Pantel,et al.  From Frequency to Meaning: Vector Space Models of Semantics , 2010, J. Artif. Intell. Res..

[19]  Stephen Clark,et al.  The Frobenius anatomy of word meanings II: possessive relative pronouns , 2014, J. Log. Comput..

[20]  T. Landauer,et al.  A Solution to Plato's Problem: The Latent Semantic Analysis Theory of Acquisition, Induction, and Representation of Knowledge. , 1997 .

[21]  Dimitri Kartsaklis,et al.  Reasoning about Meaning in Natural Language with Compact Closed Categories and Frobenius Algebras , 2014, ArXiv.

[22]  Mark Steedman,et al.  Information Structure and the Syntax-Phonology Interface , 2000, Linguistic Inquiry.

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