Many-valued modal non-monotonic reasoning: Sequential stable sets and logics with linear truth spaces

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dc.contributor.author Koutras, CD en
dc.contributor.author Koletsos, G en
dc.contributor.author Zachos, S en
dc.date.accessioned 2014-03-01T01:48:36Z
dc.date.available 2014-03-01T01:48:36Z
dc.date.issued 1999 en
dc.identifier.issn 01692968 en
dc.identifier.uri http://hdl.handle.net/123456789/25534
dc.relation.uri http://www.scopus.com/inward/record.url?eid=2-s2.0-0010440166&partnerID=40&md5=9ad821496dd63da37f9fa3670048d57f en
dc.subject Epistemic Logics en
dc.subject Knowledge representation en
dc.subject Many-valued Logics en
dc.subject Modal Non-monotonic Logics en
dc.subject Non-monotonic Reasoning en
dc.title Many-valued modal non-monotonic reasoning: Sequential stable sets and logics with linear truth spaces en
heal.type journalArticle en
heal.publicationDate 1999 en
heal.abstract A family of many-valued modal logics which correspond to possible-worlds models with many-valued accessibility relations, has been recently proposed by M. Fitting [7, 8]. Non-monotonic extensions of these logics are introduced with a fixpoint construction à la McDermott & Doyle and employ sequential belief sets as epistemic states [9]. In this paper we take a logical investigation of many-valued modal non-monotonic reasoning in Fitting's formal framework. We examine the notion of MV-stable sets which emerges as a sequential many-valued analog of Stalnaker-Moore stable sets and prove that several attractive epistemic properties are essentially retained in the many-valued setting, esp. when focusing on a syntactically simple epistemic fragment of MV-stable sets. We show that MV-stable sets are always closed under S4 consequence and identify three sufficient conditions for capturing axioms of negative introspection. Also, the relation of MV-stable sets to many-valued analogs of classical S5 models and to many-valued extensions of universal models is discussed. Finally, we pay special attention to the subclass of logics built on linear Heyting algebras and show that inside this subclass, the situation is very similar - in many respects - to the machinery devised by W. Marek, G. Schwarz and M. Truszczyński. In particular, the normal fragments of the two important classical ranges of modal non-monotonic logics remain intact: many-valued autoepistemic logic is captured by any non-monotonic logic in K5 - KD45 and many-valued reflexive autoepistemic logic corresponds to KTw5 - Sw5. en
heal.journalName Fundamenta Informaticae en
dc.identifier.volume 38 en
dc.identifier.issue 3 en
dc.identifier.spage 281 en
dc.identifier.epage 324 en

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