Inductive Generalization in Logical Inference and Techniques to Estimate It

Boris A. Kulik (Institute of Problems in Mechanical Engineering, Russian Academy of Sciences)
Alexander Ya. Fridman (Institute for Informatics and Mathematical Modelling, Kola Science Centre of RAS)

Bulletin of Electrical Engineering and Informatics
Vol 3, No 3: September 2014

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.