Towards an ontology of approximate reason

  • Authors:

  • James F. Peters;Andrzej Skowron;Jaroslaw Stepaniuk;Sheela Ramanna

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg Manitoba R3T 5V6 Canada;Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland;Department of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland;Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg Manitoba R3T 5V6 Canada

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2002

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Abstract

This article introduces structural aspects in an ontology of approximate reason. The basic assumption in this ontology is that approximate reason is a capability of an agent. Agents are designed to classify information granules derived from sensors that respond to stimuli in the environment of an agent or received from other agents. Classification of information granules is carried out in the context of parameterized approximation spaces and a calculus of granules. Judgment in agents is a faculty of thinking about (classifying) the particular relative to decision rules derived from data. Judgment in agents is reflective, but not in the classical philosophical sense (e.g., the notion of judgment in Kant). In an agent, a reflective judgment itself is an assertion that a particular decision rule derived from data is applicable to an object (input). That is, a reflective judgment by an agent is an assertion that a particular vector of attribute (sensor) values matches to some degree the conditions for a particular rule. In effect, this form of judgment is an assertion that a vector of sensor values reflects a known property of data expressed by a decision rule. Since the reasoning underlying a reflective judgment is inductive and surjective (not based on a priori conditions or universals), this form of judgment is reflective, but not in the sense of Kant. Unlike Kant, a reflective judgment is surjective in the sense that it maps experimental attribute values onto the most closely matching descriptors (conditions) in the derived rule. Again, unlike Kant's notion of judgment, a reflective judgment is not the result of searching for a universal that pertains to a particular set of values of descriptors. Rather, a reflective judgment by an agent is a form of recognition that a particular vector of sensor values pertains to a particular rule in some degree. This recognition take the form of an assertion that a particular descriptor vector is associated with a particular decision rule. These considerations can be repeated to other forms of classifiers besides those defined by decision rules.