Abstract
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.
Highlights
Categorization is the process in which ideas and objects are recognized, differentiated, and understood [1]
The proposed formalism is within the Boolean frame
The proposed formalism is within the Boolean frame, securing the principles of categorization
Summary
Categorization is the process in which ideas and objects are recognized, differentiated, and understood [1]. The meanings of the categories can be explained by the operations of classical logic Such formalization implies that the categorization process is governed by the laws of Boolean algebra, among which the laws of thought are fundamental. In the case of gradation, an infinite number of objects can be differentiated inside one category This implies that the categorization based on gradation can provide maximum information about the world with the least cognitive effort. The proposed formalism is within the Boolean frame, securing the principles of categorization This shows that Boolean laws are universal in categorization— valid in the classical and the prototype theory. Such laws can be considered as the fundamental laws governing the categorization process. The simple artificial cognitive system which mimics human categorization ability is proposed
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