Hierarchical conceptual spaces for concept combination

We introduce a hierarchical framework for conjunctive concept combination based on conceptual spaces and random set theory. The model has the flexibility to account for composition of concepts at various levels of complexity. We show that the conjunctive model includes linear combination as a special case, and that the more general model can account for non-compositional behaviours such as overextension, non-commutativity, preservation of necessity and impossibility of attributes and to some extent, attribute loss or emergence. We investigate two further aspects of human concept use, the conjunction fallacy and the 'guppy effect'.

[1]  H. Kamp,et al.  Prototype theory and compositionality , 1995, Cognition.

[2]  Mirella Lapata,et al.  Composition in Distributional Models of Semantics , 2010, Cogn. Sci..

[3]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[4]  Diederik Aerts,et al.  A theory of concepts and their combinations I: The structure of the sets of contexts and properties , 2005 .

[5]  K. Fine.  Vagueness, truth and logic , 1975, Synthese.

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

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

[8]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[9]  Edward E. Smith,et al.  On the adequacy of prototype theory as a theory of concepts , 1981, Cognition.

[10]  Igor Douven,et al.  What Verities May Be , 2017 .

[11]  Jonathan Lawry,et al.  Uncertainty modelling for vague concepts: A prototype theory approach , 2009, Artif. Intell..

[12]  Jonathan Lawry.  Modelling and Reasoning with Vague Concepts , 2006, Studies in Computational Intelligence.

[13]  Marco Baroni,et al.  Nouns are Vectors, Adjectives are Matrices: Representing Adjective-Noun Constructions in Semantic Space , 2010, EMNLP.

[14]  H. Kamp.  Two theories about adjectives , 2013 .

[15]  Jonathan Lawry,et al.  A label semantics approach to linguistic hedges , 2014, Int. J. Approx. Reason..

[16]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[17]  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.

[18]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

[19]  Richard Montague,et al.  The Proper Treatment of Quantification in Ordinary English , 1973 .

[20]  N. Foo.  Conceptual Spaces—The Geometry of Thought , 2022 .

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

[22]  Peter Gärdenfors,et al.  Event structure, conceptual spaces and the semantics of verbs , 2012 .

[23]  Daniel N. Osherson,et al.  Conceptual Combination with Prototype Concepts , 1984, Cogn. Sci..

[24]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[25]  Igor Douven,et al.  What Is Graded Membership , 2014 .

[26]  Michael Freund,et al.  On the notion of concept I , 2008, Artif. Intell..

[27]  Martha Lewis.  Modelling compositionality of vague concepts , 2015 .

[28]  Jonathan Lawry,et al.  Emerging Dimension Weights in a Conceptual Spaces Model of Concept Combination , 2016, ArXiv.

[29]  Laurianne Sitbon,et al.  Quantum-like non-separability of concept combinations, emergent associates and abduction , 2012, Log. J. IGPL.

[30]  E. Rosch.  Cognitive Representations of Semantic Categories. , 1975 .

[31]  John T. Rickard,et al.  Reformulation of the theory of conceptual spaces , 2007, Inf. Sci..

[32]  Curt Burgess,et al.  Producing high-dimensional semantic spaces from lexical co-occurrence , 1996 .

[33]  J. A. W. Kamp,et al.  Formal semantics of Natural Language: Two theories about adjectives , 1975 .

[34]  James A. Hampton,et al.  Testing the Prototype Theory of Concepts , 1995 .

[35]  Diederik Aerts,et al.  Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought , 2012, Top. Cogn. Sci..

[36]  Grant DA-AR.  A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges , 2015 .

[37]  George Lakoff,et al.  Hedges: A study in meaning criteria and the logic of fuzzy concepts , 1973, J. Philos. Log..

[38]  Yorick Wilks,et al.  New Mexico State University Computing Research Laboratory , 1988, HLT.

[39]  J. Hampton.  Inheritance of attributes in natural concept conjunctions , 1987, Memory & cognition.

[40]  Jonathan Lawry.  Modelling and Reasoning with Vague Concepts (Studies in Computational Intelligence) , 2006 .

[41]  Benjamin Adams,et al.  A Metric Conceptual Space Algebra , 2009, COSIT.

[42]  Steven Schockaert,et al.  Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces , 2013, Artif. Intell..

[43]  Didier Dubois,et al.  The three semantics of fuzzy sets , 1997, Fuzzy Sets Syst..

[44]  Janet Aisbett,et al.  A general formulation of conceptual spaces as a meso level representation , 2001, Artif. Intell..

[45]  Lance J. Rips,et al.  Structure and process in semantic memory: A featural model for semantic decisions. , 1974 .

[46]  J. Bullinaria,et al.  Extracting semantic representations from word co-occurrence statistics: A computational study , 2007, Behavior research methods.

[47]  Steven Schockaerta,et al.  Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces , 2013 .

[48]  Richard A. Frost,et al.  Adjectives: A Uniform Semantic Approach , 2005, Canadian AI.

[49]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[50]  Diederik Aerts,et al.  Quantum Structure in Cognition , 2008, 0805.3850.

[51]  Peter Gärdenfors,et al.  Using Conceptual Spaces to Model Actions and Events , 2012, J. Semant..

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

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