Semantics of Analogies from a Logical Perspective

A number of different approaches to model analogies and analogical reasoning in AI have been proposed, applying different knowledge representation and mapping strategies. Nevertheless, analogies still seem to be hard to grasp from a formal perspective, with no known treatment in the literature of, in particular, their formal semantics, though the empirical treatments involving human subjects are abundant. In this paper we present a framework that allows to analyze the syntax and the semantics of analogies in a universal logic-based setting without committing ourselves to a specific type of logic. We show that the syntactic process of analogy-making by finding a generalization can be given a sensible interpretation on the semantic level based on the theory of institutions. We then apply these ideas by considering a framework of analogy-making that is based on classical first-order logic.

[1]  Ben Goertzel,et al.  Artificial General Intelligence , 2017, Lecture Notes in Computer Science.

[2]  Brian Falkenhainer,et al.  The Structure-Mapping Engine: Algorithm and Examples , 1989, Artif. Intell..

[3]  D. Hofstadter Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, Douglas Hofstadter. 1994. Basic Books, New York, NY. 512 pages. ISBN: 0-465-05154-5. $30.00 , 1995 .

[4]  J. Bermúdez Cognitive Science: An Introduction to the Science of the Mind , 2020 .

[5]  D. Gentner,et al.  The analogical mind : perspectives from cognitive science , 2001 .

[6]  J. Fodor The Modularity of mind. An essay on faculty psychology , 1986 .

[7]  John J. Clement,et al.  Creative Model Construction in Scientists and Students , 2008 .

[8]  Bipin Indurkhya,et al.  Analogical projection in pattern perception , 2003, J. Exp. Theor. Artif. Intell..

[9]  Grigore Rosu,et al.  Institution Morphisms , 2013, Formal Aspects of Computing.

[10]  R. Diaconescu Institution-independent model theory , 2008 .

[11]  B. Indurkhya Metaphor and Cognition: An Interactionist Approach , 1992 .

[12]  Alan Bundy,et al.  Dynamic, Automatic, First-Order Ontology repair by Diagnosis of Failed Plan Execution , 2007, Int. J. Semantic Web Inf. Syst..

[13]  Kai-Uwe Kühnberger,et al.  Creativity, Cognitive Mechanisms, and Logic , 2012, AGI.

[14]  Analogies : Integrating Multiple Cognitive Abilities Guest Editorial Why Analogy ? , 2022 .

[15]  John E. Hummel,et al.  LISA: A computational model of analogical inference and schema induction , 1996 .

[16]  B. Indurkhya,et al.  Metaphor and Cognition: An Interactionist Approach , 1993, CL.

[17]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[18]  Alan Bundy,et al.  Higher-order Representation and Reasoning for Automated Ontology Evolution , 2010, KEOD.

[19]  Alexander A. Petrov,et al.  Integration of Memory and Reasoning in Analogy-Making: The AMBR Model , 2000 .

[20]  Ben Goertzel,et al.  Artificial General Intelligence (Cognitive Technologies) , 2007 .