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)
Title:
NM3 - A three-valued cumulative non-monotonic formalism
Department:
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Publication type:
Conference paper (Refereed)
Language:
English
In:
Logics in AI, European Workshop (JELIA)
Editor:
Jan van Eijck
Publisher: Springer Berlin/Heidelberg
Series:
Lecture Notes in Artificial Intelligence, ISSN 0302-9743; 478
Pages:
196-211
Year of publ.:
1990
URI:
urn:nbn:se:liu:diva-41412
Permanent link:
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-41412
ISBN:
978-3-540-53686-4
Local ID:
56311
Subject category:
Computer Science
SVEP category:
Computer science
Abstract(en) :

In this paper, we propose a formalization of non-monotonic reasoning using a three-valued logic based on the strong definitions of Kleene. We start by extending Kleene's three-valued logic with an "external negation" connective where ~ alpha is true when alpha is false or unknown. In addition, a default operator D is added where D alpha is interpreted as "alpha is true by default". The addition of the default operator increases the expressivity of the language, where statements such as "alpha is not a default" are directly representable. The logic has an intuitive model theoretic semantics without any appeal to the use of a fixpoint semantics for the default operator. The semantics is based on the notion of preferential entailment, where a set of sentences Gamma preferentially entails a sentence alpha, if and only if a preferred set of the models of Gamma are models of alpha. We also show that the logic belongs to the class of cumulative non-monotonic formalisms which are a subject of current interest.

Available from:
2009-10-10
Created:
2009-10-10
Last updated:
2012-01-18
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