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Logical Inference and Defeasible Reasoning in N-tuple Algebra
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Author(s): Boris Kulik (Institute of Problems in Mechanical Engineering, Russian Academy of Sciences (RAS), Russia), Alexander Fridman (Institute for Informatics and Mathematical Modelling, Russia)and Alexander Zuenko (Institute for Informatics and Mathematical Modelling, Russia)
Copyright: 2013
Pages: 27
Source title:
Diagnostic Test Approaches to Machine Learning and Commonsense Reasoning Systems
Source Author(s)/Editor(s): Xenia Naidenova (Military Medical Academy, Russia)and Dmitry I. Ignatov (National Research University Higher School of Economics, Russia)
DOI: 10.4018/978-1-4666-1900-5.ch005
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Abstract
This chapter examines the usage potential of n-tuple algebra (NTA) developed by the authors as a theoretical generalization of structures and methods applied in intelligence systems. NTA supports formalization of a wide set of logical problems (abductive and modified conclusions, modelling graphs, semantic networks, expert rules, etc.). This chapter mostly focuses on implementation of logical inference and defeasible reasoning by means of NTA. Logical inference procedures in NTA 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. Inference methods consider (above feasibility of certain substitutions) inner structure of knowledge to be processed, thus providing faster solving of standard logical analysis tasks. Matrix properties of NTA objects allow decreasing the complexity of intellectual procedures. As for making databases more intelligent, NTA can be considered as an extension of relational algebra to knowledge processing.
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