A first-order logic for multi-algebras.
Cīrulis, Jānis (2004)
Novi Sad Journal of Mathematics
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Cīrulis, Jānis (2004)
Novi Sad Journal of Mathematics
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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.
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...
Jun Tao Wang, Xiao Long Xin, Arsham Borumand Saeid (2016)
Open Mathematics
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The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are...
Francesc Esteva, Lluis Godo (1999)
Mathware and Soft Computing
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In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law. ...
Wiktor Bartol, Ewa Orłowska, Andrzej Skowron (1999)
Banach Center Publications
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Tarek Sayed Ahmed (2002)
Fundamenta Mathematicae
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SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends...
Figallo, Aldo V. (1992)
Portugaliae mathematica
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Cecylia Rauszer (1993)
Banach Center Publications
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Giuliana Gnani, Giuliano Mazzanti (1999)
Rendiconti del Seminario Matematico della Università di Padova
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E. G. K. López-Escobar, Francisco Miraglia
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Kiyoshi Iséki (1982)
Banach Center Publications
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