Algebraic Approach to Combining Logical Inference with Defeasible Reasoning

Boris A. Kulik, Alexander Ya. Fridman, Alexander A. Zuenko

Abstract


The study describes new capabilities of N-tuple algebra (NTA) belonging to the class of Boolean algebras and developed by the authors as a theoretical generalization of structures and methods applied in intelligence systems. NTA supports formalization and solving a wide set of logical problems (abductive and modified conclusions, modelling of graphs, semantic networks, expert rules, etc.). Here we mostly focus on unified implementation of logical inference and defeasible reasoning by means of NTA. In NTA, reasoning procedures can include, besides the known logical calculus methods, new algebraic methods for checking correctness of a consequence or for finding corollaries to a given axiom system. All NTA reasoning techniques have clear interpretations within classical logic.

Keywords


data processing; knowledge representation; intelligence system; flexible universe; n-ary relation; general theory of relations; logical inference; defeasible reasoning

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Systema: connecting matter, life, culture and technology (ISSN: 2305-6991) is a peer-reviewed, open-access journal. All journal content, except where otherwise noted, is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.