LiU Electronic Press
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Author:
Doherty, Patrick (Linköping University, The Institute of Technology) (Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab)
Szalas, Andrzej (Linköping University, The Institute of Technology) (Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab)
Title:
A correspondence framework between three-valued logics and similarity-based approximate reasoning
Department:
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Publication type:
Article in journal (Refereed)
Language:
English
Publisher: IOS Press
Status:
Published
In:
Fundamenta Informaticae(ISSN 0169-2968)
Volume:
75
Issue:
1-4
Pages:
179-193
Year of publ.:
2007
URI:
urn:nbn:se:liu:diva-48028
Permanent link:
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-48028
Subject category:
Engineering and Technology
SVEP category:
TECHNOLOGY
Keywords(en) :
approximate reasoning, rough sets, similarity relation, three-valued logics
Abstract(en) :

This paper focuses on approximate reasoning based on the use of similarity spaces. Similarity spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak [17, 18]. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logic which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between approximate relations, similarity spaces and three-valued logics. Using ideas from correspondence theory for modal logics and constraints on an accessibility relation, we develop an analogous framework for three-valued logics and constraints on similarity relations. In this manner, we can provide a tool which helps in determining the proper three-valued logical reasoning engine to use for different classes of approximate relations generated via specific types of similarity spaces. Additionally, by choosing a three-valued logic first, the framework determines what constraints would be required on a similarity relation and the approximate relations induced by it. Such information would guide the generation of approximate relations for specific applications.

Available from:
2009-10-11
Created:
2009-10-11
Last updated:
2011-02-27
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