Helena Rasiowa, 1917-1994
Wiktor Bartol, Ewa Orłowska, Andrzej Skowron (1999)
Banach Center Publications
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Wiktor Bartol, Ewa Orłowska, Andrzej Skowron (1999)
Banach Center Publications
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Damian Niwiński, Marek Zawadowski (1999)
Banach Center Publications
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Josep Font (1993)
Banach Center Publications
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The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory...
Shokoofeh Ghorbani (2020)
Bulletin of the Section of Logic
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In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive...
Mirjana Borisavljević (2012)
Review of the National Center for Digitization
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Nebojša Ikodinović (2012)
Review of the National Center for Digitization
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Mirjana Borisavljević (2010)
Review of the National Center for Digitization
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Mirjana Borisavljević (2010)
Review of the National Center for Digitization
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Don Pigozzi, Antonino Salibra (1993)
Banach Center Publications
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The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Zoran Ognjanović (2009)
Zbornik Radova
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Cīrulis, Jānis (2004)
Novi Sad Journal of Mathematics
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Miomir S. Stanković, Radomir S. Stanković (2012)
Review of the National Center for Digitization
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Larisa Maksimova (1999)
Banach Center Publications
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We consider the families 𝓛 of propositional superintuitionistic logics (s.i.l.) and NE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between 𝓛 and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig's interpolation property (CIP), the disjunction property (DP), the Beth property (BP), Hallden-completeness...