Formalization of Human Categorization Process Using Interpolative Boolean Algebra

Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed.

[1]  Robert M. Nosofsky,et al.  Exemplar-based approach to relating categorization, identification, and recognition , 1992 .

[2]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[3]  M. K. Luhandjula.  Studies in Fuzziness and Soft Computing , 2013 .

[4]  G. Bower,et al.  THE PSYCHOLOGY OF LEARNING AND M·OTIVATION , 2001 .

[5]  Eleanor Rosch,et al.  Principles of Categorization , 1978 .

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

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

[8]  L. Zadeh.  A new direction in AI: toward a computational theory of perceptions , 2002 .

[9]  J. Hampton.  Concepts as Prototypes , 2006 .

[10]  Henri Cohen,et al.  Handbook of categorization in cognitive science , 2005 .

[11]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[12]  Fangzhen Lin.  A Planner Called R , 2001, AI Mag..

[13]  Safa R. Zaki,et al.  Exemplar and prototype models revisited: response strategies, selective attention, and stimulus generalization. , 2002, Journal of experimental psychology. Learning, memory, and cognition.

[14]  Dragan G. Radojevic.  Real-Valued Realizations of Boolean Algebras Are a Natural Frame for Consistent Fuzzy Logic , 2013, On Fuzziness.

[15]  P. N. Johnson-Laird,et al.  Mental models of Boolean concepts , 2011, Cognitive Psychology.

[16]  Dragan Radojevic.  Interpolative relations and interpolative preference structures , 2005 .

[17]  Dragan G. Radojevic,et al.  A software tool for uncertainty modeling using Interpolative Boolean algebra , 2014, Knowl. Based Syst..

[18]  Dragan Radojevic,et al.  [0,1]-VALUED LOGIC: A NATURAL GENERALIZATION OF BOOLEAN LOGIC , 2000 .

[19]  Douglas L. Medin,et al.  Context theory of classification learning. , 1978 .

[20]  D. Radojević.  Logical aggregation based on interpolative boolean algebra , 2008, SOCO 2008.

[21]  J. Feldman.  A catalog of Boolean concepts , 2003 .

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

[23]  L. A. Zadeh,et al.  A note on prototype theory and fuzzy sets , 1982, Cognition.

[24]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[25]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.