Generalized relations in linguistics & cognition

Categorical compositional models of natural language exploit grammatical structure to calculate the meaning of sentences from the meanings of individual words. This approach outperforms conventional techniques for some standard NLP tasks. More recently, similar compositional techniques have been applied to conceptual space models of cognition.

[1]  Peter Selinger,et al.  Dagger Compact Closed Categories and Completely Positive Maps: (Extended Abstract) , 2007, QPL.

[2]  Fabrizio Genovese,et al.  Custom Hypergraph Categories via Generalized Relations , 2017, CALCO.

[3]  Martha Lewis,et al.  Generalized Relations in Linguistics and Cognition , 2017, WoLLIC.

[4]  B. Coecke,et al.  Classical and quantum structuralism , 2009, 0904.1997.

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

[6]  Isar Stubbe,et al.  Categorical structures enriched in a quantaloid : categories and semicategories/ , 2003 .

[7]  Jonathan Barrett.  Information processing in generalized probabilistic theories , 2005 .

[8]  P. Gärdenfors.  The Geometry of Meaning: Semantics Based on Conceptual Spaces , 2014 .

[9]  P. Johnstone.  Sketches of an Elephant , 2007 .

[10]  Brendan Fong,et al.  The algebra of open and interconnected systems , 2016, 1609.05382.

[11]  Mehrnoosh Sadrzadeh,et al.  Many Valued Generalised Quantifiers for Natural Language in the DisCoCat Model , 2016 .

[12]  A. Tversky.  Features of Similarity , 1977 .

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

[14]  W. C. Mcginnis.  Ideals , 1925, Free Speech.

[15]  Aleks Kissinger,et al.  Picturing Quantum Processes by Bob Coecke , 2017 .

[16]  I. Moerdijk,et al.  Sheaves in geometry and logic: a first introduction to topos theory , 1992 .

[17]  J. Hampton,et al.  Disjunction of natural concepts , 1988, Memory & cognition.

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

[19]  Martha Lewis,et al.  Graded Entailment for Compositional Distributional Semantics , 2016, ArXiv.

[20]  B. Coecke,et al.  Categories for the practising physicist , 2009, 0905.3010.

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

[22]  Michael J. Spivey,et al.  Graded motor responses in the time course of categorizing atypical exemplars , 2007, Memory & cognition.

[23]  Martha Lewis,et al.  Interacting Conceptual Spaces I : Grammatical Composition of Concepts , 2017, Conceptual Spaces: Elaborations and Applications.

[24]  Brendan Fong,et al.  A Compositional Framework for Passive Linear Networks , 2015, 1504.05625.

[25]  Stephen Clark,et al.  A quantum teleportation inspired algorithm produces sentence meaning from word meaning and grammatical structure , 2013, ArXiv.

[26]  Aleks Kissinger,et al.  Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning , 2017 .

[27]  Filippo Bonchi,et al.  Full Abstraction for Signal Flow Graphs , 2015, POPL.

[28]  G. Ludwig.  An axiomatic basis for quantum mechanics , 1985 .

[29]  J. Hampton.  Overextension of Conjunctive Concepts: Evidence for a Unitary Model of Concept Typicality and Class Inclusion , 1988 .

[30]  P. Johnstone,et al.  REVIEWS-Sketches of an elephant: A topos theory compendium , 2003 .

[31]  Edward E. Smith,et al.  Gradedness and conceptual combination , 1982, Cognition.

[32]  Martha Lewis,et al.  Interacting Conceptual Spaces , 2016, SLPCS@QPL.

[33]  Brendan Fong,et al.  A compositional framework for Markov processes , 2015, 1508.06448.

[34]  Sally Popkorn,et al.  A Handbook of Categorical Algebra , 2009 .

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

[36]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[37]  Dimitri Kartsaklis,et al.  A Frobenius Model of Information Structure in Categorical Compositional Distributional Semantics , 2015, ArXiv.

[38]  L. Barsalou.  Ideals, central tendency, and frequency of instantiation as determinants of graded structure in categories. , 1985, Journal of experimental psychology. Learning, memory, and cognition.

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

[41]  Peter Gärdenfors,et al.  Conceptual spaces - the geometry of thought , 2000 .

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

[43]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

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

[45]  John C. Baez,et al.  Categories in Control , 2014, 1405.6881.

[46]  Theo Buehler,et al.  Exact Categories , 2008, 0811.1480.

[47]  Dirk Hofmann,et al.  Monoidal topology : a categorical approach to order, metric, and topology , 2014 .

[48]  Samson Abramsky,et al.  A categorical semantics of quantum protocols , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

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

[50]  Comparing Meaning in Language and Cognition : P-Hyponymy , Concept Combination , Asymmetric Similarity Candidate , 2016 .

[51]  Aleks Kissinger,et al.  Finite matrices are complete for (dagger-)hypergraph categories , 2014, 1406.5942.