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Size and logic

Dov M. Gabbay & Karl Schlechta

Review of Symbolic Logic 2 (2):396-413 (2009)

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Reactive preferential structures and nonmonotonic consequence.Dov M. Gabbay & Karl Schlechta - 2009 - Review of Symbolic Logic 2 (2):414-450.details We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. These are networks with arrows recursively leading to other arrows etc. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can the strong coherence properties of preferential structures by higher arrows, that is, arrows, which do not go (...) Download Export citation Bookmark 6 citations
Semantic interpolation.Dov M. Gabbay & Karl Schlechta - 2010 - Journal of Applied Non-Classical Logics 20 (4):345-371.details The problem of interpolation is a classical problem in logic. Given a consequence relation \|~ and two formulas φ and ψ with φ \|~ ψ we try to find a “simple" formula α such that φ \|~ α \|~ ψ. “Simple" is defined here as “expressed in the common language of φ and ψ". Non-monotonic logics like preferential logics are often a mixture of a non-monotonic part with classical logic. In such cases, it is natural examine also variants of the (...) Download Export citation Bookmark 2 citations
Modal Logics of Reactive Frames.Dov M. Gabbay & Sérgio Marcelino - 2009 - Studia Logica 93 (2-3):405-446.details A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by (...) Download Export citation Bookmark 4 citations

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