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NM3 - A three-valued cumulative non-monotonic formalism
1990 (English)In: Logics in AI, European Workshop (JELIA) / [ed] Jan van Eijck, Springer Berlin/Heidelberg, 1990, 196-211Konferensbidrag (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.

Series
Lecture Notes in Artificial Intelligence, ISSN 0302-9743 ; 478
National Category
Computer Science
Identifiers
urn:nbn:se:liu:diva-41412 (URN)10.1007/BFb0018442 (DOI)56311 (Local ID)978-3-540-53686-4 (ISBN)oai:DiVA.org:liu-41412 (OAI)
Available from2009-10-10 Created:2009-10-10 Last updated:2012-01-18

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Doherty, Patrick
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The Institute of TechnologyKPLAB - Knowledge Processing Lab
Computer Science

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