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

Koutras, CD; Koletsos, G; Zachos, S

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	https://dspace.lib.ntua.gr/xmlui/handle/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