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On Jaśkowski-type semantics for the intuitionistic propositional logic

Stanisław J. Surma, Andrzej Wroński & Stanisław Zachorowski

Studia Logica 34 (2):145-148 (1975)

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Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wiendetails The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) Download Export citation Bookmark 17 citations
Admissibility and refutation: some characterisations of intermediate logics.Jeroen P. Goudsmit - 2014 - Archive for Mathematical Logic 53 (7-8):779-808.details Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...) Download Export citation Bookmark 3 citations
On the degree of complexity of sentential logics. A couple of examples.Jacek Hawranek & Jan Zygmunt - 1981 - Studia Logica 40 (2):141 - 153.details The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is (...) Download Export citation Bookmark 5 citations
Number of Extensions of Non-Fregean Logics.Joanna Golińska-Pilarek & Taneli Huuskonen - 2005 - Journal of Philosophical Logic 34 (2):193-206.details We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF. Download Export citation Bookmark 5 citations
Finite axiomatization for some intermediate logics.I. Janioka-Żuk - 1980 - Studia Logica 39 (4):415-423.details LetN. be the set of all natural numbers, and letD n * = {k N k\|n} {0} wherek¦n if and only ifn=k.x f or somexN. Then, an ordered setD n * = D n , n, wherex ny iffx¦y for anyx, yD n , can easily be seen to be a pseudo-boolean algebra.In [5], V.A. Jankov has proved that the class of algebras {D n * nB}, whereB =, {k N is finitely axiomatizable. Download Export citation Bookmark

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