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Flat modal fixpoint logics with the converse modality
Stockholm University, Faculty of Humanities, Department of Philosophy.
Number of Authors: 12018 (English)In: Journal of logic and computation (Print), ISSN 0955-792X, E-ISSN 1465-363X, Vol. 28, no 6, p. 1065-1097Article in journal (Refereed) Published
Abstract [en]

We prove a generic completeness result for a class of modal fixpoint logics corresponding to flat fragments of the two-way mu-calculus, with the restriction that the fixpoint connectives involved must be disjunctive formulas. This extends earlier work by Santocanale and Venema. We observe that Santocanale and Venema's proof that least fixpoints in the free algebras of flat fixpoint logics are constructive, using finitary adjoints, no longer works when the converse modality is introduced. Instead, our completeness proof directly constructs a model for a consistent formula, using the induction rule in a way that is similar to the standard completeness proof for propositional dynamic logic. This approach is combined with the concept of a focus, which has previously been used in tableau-based reasoning for modal fixpoint logics, and the use of networks, which is a well-known tool for proving completeness of modal logics.

Place, publisher, year, edition, pages
2018. Vol. 28, no 6, p. 1065-1097
Keywords [en]
Modal fixpoint logic, mu-calculus, converse modality, completeness, network
National Category
Computer and Information Sciences Philosophy
Identifiers
URN: urn:nbn:se:su:diva-165744DOI: 10.1093/logcom/exy016ISI: 000454695000004OAI: oai:DiVA.org:su-165744DiVA, id: diva2:1285556
Available from: 2019-02-04 Created: 2019-02-04 Last updated: 2019-02-04Bibliographically approved

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