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A Note on the Intuitionistic Logic of False Belief

Tomasz Witczak

Bulletin of the Section of Logic > 2022 > 51 > 1 > 57-71

In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ is not satisfied in a given world, but we still believe in it (or we think that it should be accepted). Another interpretations are also possible: e.g. that we do not accept $\varphi$ but...

article

Weakly Free Multialgebras

Marcelo Esteban Coniglio, Guilherme Vicentin de Toledo

Bulletin of the Section of Logic > 2022 > 51 > 1 > 109-141

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are...

article

A Variant of Material Connexive Logic

Alexander Belikov, Dmitry Zaitsev

Bulletin of the Section of Logic > 2022 > 51 > 2

The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles...

article

Ternary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B

Sandra M. López

Bulletin of the Section of Logic > 2022 > 51 > 1 > 27-56

Six interesting variants of the logics BN4 and E4-which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively-were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics...

article

Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts

Torben Braüner

Bulletin of the Section of Logic > 2022 > 51 > 2 > 143-162

This paper is about non-labelled proof-systems for hybrid logic, that is, proofsystems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that nonlabelled...

article

Proof Compression and NP Versus PSPACE II: Addendum

Lew Gordeev, Edward Hermann Haeusler

Bulletin of the Section of Logic > 2022 > 51 > 2 > 197-205

In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic (HSC) with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction (ND). In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea (due to the second author)...

article

Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles

Nathan Grieve

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 95-119

We study the property of continuous Castelnuovo-Mumford regularity, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives a novel description thereof. It is expressed in terms of certain normalized polynomial functions that are obtained via the Wedderburn decomposition of the...

article

Metrizable space of multivalued maps

Mirosław Ślosarski

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 77-93

In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homotopy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric.

article

Equivalential algebras with conjunction on the regular elements

Sławomir Przybyło

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 63-75

We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.

article

Examples of non connective C*-algebras

Anna Gąsior, Andrzej Szczepański

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 57-61

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

article

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Farid Nouioua, Bilal Basti

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 43-56

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

article

System of boundary random fractional differential equations via Hadamard derivative

Zakaria Malki, Farida Berhoun, Abdelghani Ouahab

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 17-41

We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

article

Soju Filters in Hoop Algebras

Rajab Ali Borzooei, Gholam Reza Rezaei, Mona Aaly Kologhani, Young Bae Jun

Bulletin of the Section of Logic > 2021 > 50 > 1 > 97-123

The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

article

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

Paweł Płaczek

Bulletin of the Section of Logic > 2021 > 50 > 1 > 55-80

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...

article

A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics

Natalya Tomova

Bulletin of the Section of Logic > 2021 > 50 > 1 > 35-53

In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two...

article

On GE-algebras

Ravikumar Bandaru, Arsham Borumand Saeid, Young Bae Jun

Bulletin of the Section of Logic > 2021 > 50 > 1 > 81-96

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive...

article

Projections of measures with small supports

Bilel Selmi

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 5-15

In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.

article

Towards a Logic of Value and Disagreement via Imprecise Measures

Federico L. G. Faroldi

Bulletin of the Section of Logic > 2021 > 50 > 2 > 131-149

After putting forward a formal account of value disagreement via imprecise measures, I develop a logic of value attribution and of (dis)agreement based on (exact) truthmaker semantics.

article

Extended MR with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena

Aleksander Parol, Krzysztof Pietrowicz, Joanna Szalacha-Jarmużek

Bulletin of the Section of Logic > 2021 > 50 > 2 > 205-227

In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These expressions allow, inter alia, to consider different points of view of social entities (humanistic coefficient). In the article, we perform a metalogical analysis of this logic. Finally,...

article

A Note on 3×3-valued Łukasiewicz Algebras with Negation

Carlos Gallardo, Alicia Ziliani

Bulletin of the Section of Logic > 2021 > 50 > 3 > 289-298

In 2004, C. Sanza, with the purpose of legitimizing the study of $n\times m$-valued Łukasiewicz algebras with negation (or $\mathbf{NS}_{n\times m}$-algebras) introduced $3 \times 3$-valued Łukasiewicz algebras with negation. Despite the various results obtained about $\mathbf{NS}_{n\times m}$-algebras, the structure of the free algebras for this variety has not been determined yet. She only...

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Search results

A Note on the Intuitionistic Logic of False Belief

Weakly Free Multialgebras

A Variant of Material Connexive Logic

Ternary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B

Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts

Proof Compression and NP Versus PSPACE II: Addendum

Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles

Metrizable space of multivalued maps

Equivalential algebras with conjunction on the regular elements

Examples of non connective C*-algebras

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

System of boundary random fractional differential equations via Hadamard derivative

Soju Filters in Hoop Algebras

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

A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics

On GE-algebras

Projections of measures with small supports

Towards a Logic of Value and Disagreement via Imprecise Measures

Extended MR with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena

A Note on 3×3-valued Łukasiewicz Algebras with Negation

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