Inductive Generalization in Logical Inference and Techniques to Estimate It

Boris A. Kulik, Alexander Ya. Fridman

Abstract


The paper presents a novel approach to problems of deductive reasoning in frames of n-tuple algebra (NTA) earlier developed by the authors. Investigations of such problems let us determine the minimal consequence in logical inference and develop techniques to find it. Besides, we have proved that many formally correct consequences are inductive generalizations of this minimal consequence. An NTA-based method is proposed to obtain a numerical estimation for the degree of such an inductive generalization. In particular, it becomes possible to predict the number of consequences for a given system of premises and the share of a minimal consequence in a universe.

Keywords


deductive logical inference, n-tuple algebra, minimal consequence, inductive generalization, numerical measure

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References


Kulik B, Fridman A, Zuenko A. Algebraic Approach to Logical Inference Implementation. Computing and Informatics (CAI), Slovakia. 2012; 31(6): 1295-1328.

Kulik B, Fridman A., Zuenko A.: Logical Inference and Defeasible Reasoning in N-tuple Algebra. In: Naidenova X, Ignatov D. Editors. Diagnostic Test Approaches to Machine Learning and Commonsense Reasoning Systems. IGI Global, Hershey PA; 2013: 102-128.

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Kulik BA. N-Tuple Algebra-Based Probabilistic Logic. Computer and Systems Sciences International, Russia. 2007; 46(1): 111-120.

Kulik BA, Zuenko AA, Fridman AYa. Deductive and Revised Reasoning on the Basis of Uniform Algebraic Approach. Artificial Intelligence and Decision Making, Russia. 2013; 4: 95-105 (in Russian).




DOI: https://doi.org/10.11591/eei.v3i3.290

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