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  1. Some Useful 16-Valued Logics: How a Computer Network Should Think.Yaroslav Shramko & Heinrich Wansing - 2005 - Journal of Philosophical Logic 34 (2):121-153.
    In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = í ”íČ«(2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᔍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an (...)
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  • Gentzen-Type Methods for Bilattice Negation.Norihiro Kamide - 2005 - Studia Logica 80 (2-3):265-289.
    A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of (...)
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  • Phase Semantics and Petri Net Interpretation for Resource-Sensitive Strong Negation.Norihiro Kamide - 2006 - Journal of Logic, Language and Information 15 (4):371-401.
    Wansing’s extended intuitionistic linear logic with strong negation, called WILL, is regarded as a resource-conscious refinment of Nelson’s constructive logics with strong negation. In this paper, (1) the completeness theorem with respect to phase semantics is proved for WILL using a method that simultaneously derives the cut-elimination theorem, (2) a simple correspondence between the class of Petri nets with inhibitor arcs and a fragment of WILL is obtained using a Kripke semantics, (3) a cut-free sequent calculus for WILL, called twist (...)
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  • Bounded Linear-Time Temporal Logic: A Proof-Theoretic Investigation.Norihiro Kamide - 2012 - Annals of Pure and Applied Logic 163 (4):439-466.
  • Synthesized Substructural Logics.Norihiro Kamide - 2007 - Mathematical Logic Quarterly 53 (3):219-225.
    A mechanism for combining any two substructural logics (e.g. linear and intuitionistic logics) is studied from a proof-theoretic point of view. The main results presented are cut-elimination and simulation results for these combined logics called synthesized substructural logics.
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  • A Spatial Modal Logic with a Location Interpretation.Norihiro Kamide - 2005 - Mathematical Logic Quarterly 51 (4):331.
    A spatial modal logic is introduced as an extension of the modal logic S4 with the addition of certain spatial operators. A sound and complete Kripke semantics with a natural space interpretation is obtained for SML. The finite model property with respect to the semantics for SML and the cut-elimination theorem for a modified subsystem of SML are also presented.
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  • Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation.Dimiter Vakarelov - 2006 - Studia Logica 84 (1):105-127.
    The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.
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  • On a Logic of Involutive Quantales.Norihiro Kamide - 2005 - Mathematical Logic Quarterly 51 (6):579-585.
    The logic just corresponding to involutive quantales, which was introduced by Wendy MacCaull, is reconsidered in order to obtain a cut-free sequent calculus formulation, and the completeness theorem for this logic is proved using a new admissible rule.
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