Displaying similar documents to “A Note on Ciuciura’s mbC1”

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...

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

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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).

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

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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).

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....

Axiomatization of a Basic Logic of Logical Bilattices

Mitio Takano (2016)

Bulletin of the Section of Logic

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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.

A Post-style proof of completeness theorem for symmetric relatedness Logic S

Mateusz Klonowski (2018)

Bulletin of the Section of Logic

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One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.

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...

Super-strict Implications

Guido Gherardi, Eugenio Orlandelli (2021)

Bulletin of the Section of Logic

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This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the...

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...

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.

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

Paweł Płaczek (2021)

Bulletin of the Section of Logic

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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....

Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations

Satoru Niki (2020)

Bulletin of the Section of Logic

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We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.