Displaying similar documents to “An Alternative Natural Deduction for the Intuitionistic Propositional Logic”

A Modified Subformula Property for the Modal Logic S4.2

Mitio Takano (2019)

Bulletin of the Section of Logic

Similarity:

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...

An Investigation into Intuitionistic Logic with Identity

Szymon Chlebowski, Dorota Leszczyńska-Jasion (2019)

Bulletin of the Section of Logic

Similarity:

We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.

Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

Wojciech Buszkowski (2017)

Bulletin of the Section of Logic

Similarity:

In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.

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

Javier Legris, Jorge A. Molina (2001)

Philosophia Scientiae

Similarity:

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...

New Modification of the Subformula Property for a Modal Logic

Mitio Takano (2020)

Bulletin of the Section of Logic

Similarity:

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.

From Intuitionism to Brouwer's Modal Logic

Zofia Kostrzycka (2020)

Bulletin of the Section of Logic

Similarity:

We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded...

Grzegorczyk’s Logics. Part I

Taneli Huuskonen (2015)

Formalized Mathematics

Similarity:

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...

One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity

Paweł Płaczek (2021)

Bulletin of the Section of Logic

Similarity:

Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics....

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

Janusz Ciuciura (2017)

Bulletin of the Section of Logic

Similarity:

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.

Axiomatization of a Basic Logic of Logical Bilattices

Mitio Takano (2016)

Bulletin of the Section of Logic

Similarity:

A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices.

Logics that are both paraconsistent and paracomplete

Newton C.A. da Costa (1989)

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

Similarity:

The Author describes new systems of logic (called "nonalethic") which are both paraconsistent and paracomplete. These systems are connected with the logic of vagueness and with certain philosophical problems (e.g. with some aspects of Hegel's logic).