(Formula presented.) is the modal logic of directed partial pre-orders and/or the modal logic of reflexive and transitive relational frames with a final cluster. It holds a distinguished position in philosophical logi...
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In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fittinǵs many-valued modal languages. These languages were introduced by M. Fitting in the early...
详细信息
In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fittinǵs many-valued modal languages. These languages were introduced by M. Fitting in the early ́90s and are built on Heyting algebras which serve as the space of truth values. The possible-worlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of many-valued accessibility relation. Weak axioms of the form we treat here have been examined from the completeness perspective and further explored for applications in non-monotonic reasoning. Here, we introduce more weak many-valued modal axioms and prove a frame correspondence result for all of them. The classes of corresponding labelled frames possess algebraic properties which are strongly reminiscent of many classical ones, such as the Church-Rosser property, reflexivity, transitivity, partial functionality, etc.
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