Displaying similar documents to “A completeness theorem in the modal logic of programs”

Intuitionistic logic considered as an extension of classical logic : some critical remarks

Javier Legris, Jorge A. Molina (2001)

Philosophia Scientiae

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In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection...

Identity, equality, nameability and completeness. Part II

María Manzano, Manuel Crescencio Moreno (2018)

Bulletin of the Section of Logic

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This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity...

Universality of Logic

Jan Woleński (2017)

Bulletin of the Section of Logic

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This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity (truth in all models). All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic....

Grzegorczyk’s Logics. Part I

Taneli Huuskonen (2015)

Formalized Mathematics

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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...

Logic of existence and logic of knowledge. Epistemic and non epistemic aspects of logic

Michel Bourdeau (2003)

Philosophia Scientiae

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Contrairement à ce qui a parfois été dit, la logique classique et la logique intuitionniste ne s’opposent pas comme une logique de l’existence à une logique de la connaissance. Les considérations épistémologiques trouvent naturellement leur place dans le cadre de la logique classique, sans qu’il soit nécessaire de faire intervenir aucun principe intuitionniste ; il suffit pour cela de reconnaître que la logique ne peut se passer de la notion d’assertion, ou si l’on préfère de jugement....

New Modification of the Subformula Property for a Modal Logic

Mitio Takano (2020)

Bulletin of the Section of Logic

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A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability for the logic follows from this.