Titlebook: Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs; Ivo Düntsch,Edwin Mares Book 2022 Springer Nature Switzerl

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Beth Definability in the Logic KR,ds. Following a suggestion of Urquhart, we use modular lattices constructed by Freese to show that epimorphisms need not be surjective in a wide class of relation algebras. This class includes the Boolean monoids, and thus the Beth Definability Property fails for ..

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Geometric Models for Relevant Logics,hat an accessibility relation in such a model might satisfy. I end by showing that a set of natural conditions on an accessibility relation, motivated by geometric considerations, is jointly unsatisfiable.

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Data-Centric AI in Mechanical Engineering,n the proof of the more general result and involves slightly different techniques. We proceed in two steps: first, we show that S4 is strongly complete for the space of finite and infinite binary sequences, equipped with a natural topology; and then we show that there is an interior map from the real line onto this space.

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Tarskian Classical Relevant Logic,haracteristic for . are the ones that are characteristic for . and satisfy an extra frame condition. There are formulas in . (but not in .) that correspond to this frame condition and provide a counterexample to a theorem of T. Kowalski. The frames characteristic for ., or ., are the ones whose comp

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Algorithmic Correspondence for Relevance Logics I. The Algorithm ,idity. We also provide a detailed comparison with two earlier works, each extending the class of Sahlqvist formulae to relevance logics, and show that both are subsumed by simple subclasses of inductive formulae.