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NM3 - A three-valued cumulative non-monotonic formalism
Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
1990 (English)In: Logics in AI, European Workshop (JELIA) / [ed] Jan van Eijck, Springer Berlin/Heidelberg, 1990, 196-211 p.Conference paper (Refereed)
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.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 1990. 196-211 p.
, Lecture Notes in Artificial Intelligence, ISSN 0302-9743 ; 478
National Category
Computer Science
URN: urn:nbn:se:liu:diva-41412DOI: 10.1007/BFb0018442Local ID: 56311ISBN: 978-3-540-53686-4OAI: diva2:262264
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2012-01-18

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Doherty, Patrick
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