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A note on paracomplete logic

Newton C. A. da Costa, Diego Marconi (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota gli Autori descrivono nuovi sistemi di logica (detta «paracompleta») connessi con la logica della vaghezza («fuzzy logic») e con le logiche paraconsistenti.

Algebraic Approach to Algorithmic Logic

Grzegorz Bancerek (2014)

Formalized Mathematics

We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signature including free variables, substitution, and equality. Algorithmic logic requires a bialgebra structure...

Annihilators in BCK-algebras

Radomír Halaš (2003)

Czechoslovak Mathematical Journal

We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra 𝒜 . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice 𝒟 ( A ) of all deductive systems on 𝒜 . Moreover, relative annihilators of C 𝒟 ( A ) with respect to B 𝒟 ( A ) are introduced and serve as relative pseudocomplements of C w.r.t. B in 𝒟 ( A ) .

Grzegorczyk’s Logics. Part I

Taneli Huuskonen (2015)

Formalized Mathematics

This article is the second in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([9] and [10]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([11]). This part presents the syntax and axioms of Grzegorczyk’s Logic of Descriptions (LD) as originally proposed by him, as well as some theorems not depending on any semantic constructions. There are both some clear similarities and fundamental differences between LD and the non-Fregean logics introduced by...

La créativité des définitions dans les systèmes para-euclidiens

Jean-Pierre Ginisti (1991)

Mathématiques et Sciences Humaines

Cet article considère trois sortes de calcul propositionnel (mais surtout la troisième), à la fois d'un point de vue logique et d'un point de vue épistémologique : (1) les systèmes classiques qui ont les propriétés suivantes : (a) chaque axiome doit contenir seulement (ou doit être compris comme contenant seulement) des termes primitifs, (b) chaque définition est métalinguistique, (c) chaque définition est non créatrice ; (2) les systèmes de Leśnieswski qui satisfont (a) mais ni (b) ni (c), une...

Lògiques distributives i booleanes.

Ventura Verdú i Solans (1979)


Continuing the study of different types of Abstract Logics [5], and following works by Brown-Bloom [1] and Brown-Suszko [2], we analyze in this paper some logics in which, if we identify equivalent formulae by means of the consequence operator, we obtain distributive lattices or Boolean algebras.

Normal forms in partial modal logic

Jan Jaspars (1993)

Banach Center Publications

A "partial" generalization of Fine's definition [Fin] of normal forms in normal minimal modal logic is given. This means quick access to complete axiomatizations and decidability proofs for partial modal logic [Thi].

On permutographs

Thomas, Gerhard G. (1982)

Proceedings of the 10th Winter School on Abstract Analysis

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