Displaying similar documents to “Classical logic with some probability operators.”

Useful Four-Valued Extension of the Temporal Logic KtT4

Vincent Degauquier (2018)

Bulletin of the Section of Logic

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The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial...

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...

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...

A Modified Subformula Property for the Modal Logic S4.2

Mitio Takano (2019)

Bulletin of the Section of Logic

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The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of □ in some formula of S. These are just the...

Deontic Paradoxes and Tableau System for Kalinowski’s Deontic Logic K1

Janusz Ciuciura (2017)

Bulletin of the Section of Logic

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In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

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....