Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L∗, a modality that allows for the use of limited editions of contraction and permutation in the logic. Lambek Calculus has been introduced to analyse syntax of natural language and the linguistic motivation behind this modality is to extend the domain of the applicability of the calculus to fragments which witness the discontinuity phenomena. The categorical part of the semantics is a monoidal biclosed category with a !-functor, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the !-functor. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L∗: the derivation of a phrase with a parasitic gap. The efficacy of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrase one, using BERT, Word2Vec, and FastText vectors and relational tensors.

[1]  Mehrnoosh Sadrzadeh,et al.  Anaphora and Ellipsis in Lambek Calculus with a Relevant Modality: Syntax and Semantics , 2021, ArXiv.

[2]  Donald Yau,et al.  Categories , 2021, 2-Dimensional Categories.

[3]  M. Sadrzadeh,et al.  Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract) , 2021, Electronic Proceedings in Theoretical Computer Science.

[4]  Mehrnoosh Sadrzadeh,et al.  A Frobenius Algebraic Analysis for Parasitic Gaps , 2020, FLAP.

[5]  Jean-Simon Pacaud Lemay,et al.  Why FHilb is Not an Interesting (Co)Differential Category , 2020, QPL.

[6]  知秀 柴田.  5分で分かる!? 有名論文ナナメ読み：Jacob Devlin et al. : BERT : Pre-training of Deep Bidirectional Transformers for Language Understanding , 2020 .

[7]  Mehrnoosh Sadrzadeh,et al.  Evaluating Composition Models for Verb Phrase Elliptical Sentence Embeddings , 2019, NAACL.

[8]  Mehrnoosh Sadrzadeh,et al.  A Type-Driven Vector Semantics for Ellipsis with Anaphora Using Lambek Calculus with Limited Contraction , 2019, Journal of Logic, Language and Information.

[9]  Glyn Morrill,et al.  A Note on movement in logical grammar , 2019, J. Lang. Model..

[10]  Mehrnoosh Sadrzadeh,et al.  Classical Copying versus Quantum Entanglement in Natural Language: The Case of VP-ellipsis , 2018, CAPNS@QI.

[11]  M. Sadrzadeh,et al.  Sentence entailment in compositional distributional semantics , 2018, Annals of Mathematics and Artificial Intelligence.

[12]  M. Moortgat,et al.  Lexical and Derivational Meaning in Vector-Based Models of Relativisation , 2017, ArXiv.

[13]  Gijs Jasper Wijnholds,et al.  Coherent Diagrammatic Reasoning in Compositional Distributional Semantics , 2017, WoLLIC.

[14]  Glyn Morrill,et al.  Grammar logicised: relativisation , 2017 .

[15]  Glyn Morrill,et al.  On the Logic of Expansion in Natural Language , 2016, LACL.

[16]  Tomas Mikolov,et al.  Enriching Word Vectors with Subword Information , 2016, TACL.

[17]  Dimitri Kartsaklis,et al.  Sentence entailment in compositional distributional semantics , 2015, Annals of Mathematics and Artificial Intelligence.

[18]  Max I. Kanovich,et al.  Undecidability of the Lambek Calculus with a Relevant Modality , 2015, FG.

[19]  Glyn Morrill,et al.  Computational Coverage of TLG: Nonlinearity , 2015, NLCS@ICALP/LICS.

[20]  Mehrnoosh Sadrzadeh,et al.  Concrete Models and Empirical Evaluations for the Categorical Compositional Distributional Model of Meaning , 2015, CL.

[21]  Jeffrey Pennington,et al.  GloVe: Global Vectors for Word Representation , 2014, EMNLP.

[22]  Dimitri Kartsaklis,et al.  Evaluating Neural Word Representations in Tensor-Based Compositional Settings , 2014, EMNLP.

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

[24]  Anne Preller,et al.  Natural language semantics in biproduct dagger categories , 2014, J. Appl. Log..

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

[26]  Jeffrey Dean,et al.  Distributed Representations of Words and Phrases and their Compositionality , 2013, NIPS.

[27]  Dimitri Kartsaklis,et al.  Prior Disambiguation of Word Tensors for Constructing Sentence Vectors , 2013, EMNLP.

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

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

[30]  Anne Preller,et al.  Semantic Vector Models and Functional Models for Pregroup Grammars , 2011, J. Log. Lang. Inf..

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

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

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

[34]  John C. Baez,et al.  Physics, Topology, Logic and Computation: A Rosetta Stone , 2009, 0903.0340.

[35]  Christopher D. Manning,et al.  Introduction to Information Retrieval , 2008, J. Assoc. Inf. Sci. Technol..

[36]  J. Robin B. Cockett,et al.  Differential categories , 2006, Mathematical Structures in Computer Science.

[37]  Yves Lafont,et al.  Soft linear logic and polynomial time , 2004, Theor. Comput. Sci..

[38]  Martin Hyland,et al.  Glueing and orthogonality for models of linear logic , 2003, Theor. Comput. Sci..

[39]  P. Johnstone.  Sketches of an Elephant: A Topos Theory Compendium Volume 1 , 2002 .

[40]  M. Pickering,et al.  Processing ambiguous verbs: evidence from eye movements. , 2001, Journal of experimental psychology. Learning, memory, and cognition.

[41]  James H. Martin,et al.  Speech and language processing: an introduction to natural language processing, computational linguistics, and speech recognition, 2nd Edition , 2000, Prentice Hall series in artificial intelligence.

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

[43]  Michael Moortgat,et al.  Multimodal linguistic inference , 1995, J. Log. Lang. Inf..

[44]  Andre Scedrov,et al.  Bounded Linear Logic: A Modular Approach to Polynomial-Time Computability , 1992, Theor. Comput. Sci..

[45]  Glyn Morrill,et al.  Proof Figures and Structural Operators for Categorial Grammar , 1991, EACL.

[46]  Mark Steedman,et al.  Combinatory grammars and parasitic gaps , 1987 .

[47]  Ivan A. Sag,et al.  On parasitic gaps , 1983 .

[48]  J. Humphreys.  Introduction to Lie Algebras and Representation Theory , 1973 .

[49]  John B. Goodenough,et al.  Contextual correlates of synonymy , 1965, CACM.

[50]  G. Salton,et al.  A document retrieval system for man-machine interaction , 1964, ACM National Conference.

[51]  Ming-Wei Chang,et al.  BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding , 2019, NAACL.

[52]  Paul-André Melliès.  CATEGORICAL SEMANTICS OF LINEAR LOGIC , 2009 .

[53]  James Richard Curran,et al.  From distributional to semantic similarity , 2004 .

[54]  Prakash Panangaden,et al.  Fock Space: A Model of Linear Exponential Types , 1994 .

[55]  Gregory Grefenstette,et al.  Explorations in automatic thesaurus discovery , 1994 .

[56]  J. R. Firth,et al.  A Synopsis of Linguistic Theory, 1930-1955 , 1957 .

[57]  Zellig S. Harris,et al.  Distributional Structure , 1954 .

[58]  Haskell B. Curry,et al.  Church Alonzo. The weak theory of implication. Kontrolliertes Denken, Untersuchungen zum Logikkalkül unci zur Logik der Einzelwissenschaften, rotaprint, Kommissions-Verlag Karl Alber, Munich 1951, pp. 22–37 , 1953 .