Browsing Bulletin of the Section of Logic by Title
Now showing items 104123 of 189

\(n\)Fold Filters of EQAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20221014)In this paper, we apply the notion of \(n\)fold filters to the \(EQ\)algebras and introduce the concepts of \(n\)fold pseudo implicative, \(n\)fold implicative, \(n\)fold obstinate, \(n\)fold fantastic prefilters and ... 
Neighbourhood Semantics for Graded Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20210714)We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be firstorder definable but not modally definable. We ... 
A New Arithmetically Incomplete First Order Extension of Gl All Theorems of Which Have Cut Free Proofs
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Reference [12] introduced a novel formula to formula translation tool (“formulators”) that enables syntactic metatheoretical investigations of firstorder modal logics, bypassing a need to convert them first into Gentzen ... 
New Modification of the Subformula Property for a Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)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 ... 
Nilpotent Minimum Logic NM and Pretabularity
(Wydawnictwo Uniwersytetu Łódzkiego, 20200330)This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp ... 
NonFregean Logics of Analytic Equivalence (I)
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)The identity connective is usually interpreted in nonFregean logic as an operator representing the identity of situations. This interpretation is related to the modal criterion of the identity of sentence correlates, ... 
NonFregean Logics of Analytic Equivalence (II)
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)This paper presents the main assumptions of Andrzej Grzegorczyk’s last research project concerning the logic of synonymity. It shows that the basis of logic of analytic equivalence, presented in the ﬁrst part of the work, ... 
A Note on 3×3valued Łukasiewicz Algebras with Negation
(Wydawnictwo Uniwersytetu Łódzkiego, 20210527)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 ... 
A Note on Ciuciura’s mbC1
(Wydawnictwo Uniwersytetu Łódzkiego, 20191030)This note offers a nondeterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and (strong) completeness results with respect to the Hilbertstyle proof system. Moreover, based on the new ... 
A Note on Distributive Triples
(Wydawnictwo Uniwersytetu Łódzkiego, 20191030)Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note ... 
A Note on GödelDummet Logic LC
(Wydawnictwo Uniwersytetu Łódzkiego, 20210701)Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n1}\rightarrow ... 
A Note on the Intuitionistic Logic of False Belief
(Wydawnictwo Uniwersytetu Łódzkiego, 20210901)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 ... 
Omitting Types in Fragments and Extensions of First Order Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20210528)Fix \(2 < n < \omega\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for ... 
On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
(Wydawnictwo Uniwersytetu Łódzkiego, 20210721)Fix a finite ordinal \(n\geq 3\) and let \(\alpha\) be an arbitrary ordinal. Let \(\mathsf{CA}_n\) denote the class of cylindric algebras of dimension \(n\) and \(\sf RA\) denote the class of relation algebras. Let ... 
On Direct Limit Closed Classes of Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Axiomatic classes of algebras of a given type which are closed with respect to direct limits are studied in this paper. 
On GEalgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20200830)Hilbert algebras are important tools for certain investigations in intuitionistic logic and other nonclassical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GEalgebra (generalized ... 
On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames. 
On Homomorphism and Cartesian Products of Intuitionistic Fuzzy PMSsubalgebra of a PMSalgebra
(Wydawnictwo Uniwersytetu Łódzkiego, 20230421)In this paper, we introduce the notion of intuitionistic fuzzy PMSsubalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic ... 
On Implicative and Positive Implicative GE Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20230925)GE algebras (generalized exchange algebras), transitive GE algebras (tGE algebras, for short) and aGE algebras (that is, GE algebrasverifying the antisymmetry) are a generalization of Hilbert algebras. Here some properties ... 
On Injective MVModules
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)In this paper, by considering the notion of MVmodule, which is the structure that naturally correspond to lumodules over lurings, we study injective MVmodules and we investigate some conditions for constructing injective ...