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  1. Proof Systems for Exact Entailment.Johannes Korbmacher - 2023 - Review of Symbolic Logic 16 (4):1260-1295.
    We present a series of proof systems for exact entailment (i.e. relevant truthmaker preservation from premises to conclusion) and prove soundness and completeness. Using the proof systems, we observe that exact entailment is not only hyperintensional in the sense of Cresswell but also in the sense recently proposed by Odintsov and Wansing.
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  • Finite axiomatizability of logics of distributive lattices with negation.Sérgio Marcelino & Umberto Rivieccio - forthcoming - Logic Journal of the IGPL.
    This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means Hilbert-style calculi that are finite. On the negative side, we provide a syntactic condition on the equational presentation of a variety that entails failure of finite axiomatizability for the corresponding logic. An application of this result is that the logic of all distributive lattices with negation is not finitely axiomatizable; we likewise establish (...)
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  • On Magari's concept of general calculus: notes on the history of tarski's methodology of deductive sciences.S. Roberto Arpaia - 2006 - History and Philosophy of Logic 27 (1):9-41.
    This paper is an historical study of Tarski's methodology of deductive sciences (in which a logic S is identified with an operator Cn S, called the consequence operator, on a given set of expressions), from its appearance in 1930 to the end of the 1970s, focusing on the work done in the field by Roberto Magari, Piero Mangani and by some of their pupils between 1965 and 1974, and comparing it with the results achieved by Tarski and the Polish school (...)
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  • On two fragments with negation and without implication of the logic of residuated lattices.Félix Bou, Àngel García-Cerdaña & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (5):615-647.
    The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this (...)
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