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Solution to a problem of Ono and Komori

John Slaney

Journal of Philosophical Logic 18 (1):103 - 111 (1989)

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A decidable paraconsistent relevant logic: Gentzen system and Routley-Meyer semantics.Norihiro Kamide - 2016 - Mathematical Logic Quarterly 62 (3):177-189.details In this paper, the positive fragment of the logic math formula of contraction-less relevant implication is extended with the addition of a paraconsistent negation connective similar to the strong negation connective in Nelson's paraconsistent four-valued logic math formula. This extended relevant logic is called math formula, and it has the property of constructible falsity which is known to be a characteristic property of math formula. A Gentzen-type sequent calculus math formula for math formula is introduced, and the cut-elimination and decidability (...) Download Export citation Bookmark
The Role of Structural Reasoning in the Genesis of Graph Theory.Michael Arndt - 2019 - History and Philosophy of Logic 40 (3):266-297.details The seminal book on graph theory by Dénes Kőnig, published in the year 1936, collected notions and results from precursory works from the mid to late nineteenth century by Hamilton, Cayley, Sylvester and others. More importantly, Kőnig himself contributed many of his own results that he had obtained in the more than twenty years that he had been working on this subject matter. What is noteworthy is the fact that the fundamentals of what he calls directed graphs are taken almost (...) Download Export citation Bookmark
A Syntactic Approach to Maksimova's Principle of Variable Separation for Some Substructural Logics.H. Naruse, Bayu Surarso & H. Ono - 1998 - Notre Dame Journal of Formal Logic 39 (1):94-113.details Download Export citation Bookmark 2 citations
Resolution and the origins of structural reasoning: Early proof-theoretic ideas of Hertz and Gentzen.Peter Schroeder-Heister - 2002 - Bulletin of Symbolic Logic 8 (2):246-265.details In the 1920s, Paul Hertz (1881-1940) developed certain calculi based on structural rules only and established normal form results for proofs. It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory. Furthermore, it is shown that Gentzen, in his first paper of 1933, which heavily draws on Hertz, proves a normal form result which corresponds to the completeness of (...) Download Export citation Bookmark 19 citations

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