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  1. On Two Fragments with Negation and Without Implication of the Logic of Residuated Lattices.Félix Bou, Àngel García-Cerdaña & Ventura Verdú - 2005 - 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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  • 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 (...)
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