Browsing Bulletin of the Section of Logic by Title
Now showing items 86105 of 189

\(L\)Modules
(Wydawnictwo Uniwersytetu Łódzkiego, 20231204)In this paper, considering \(L\)algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)algebras (\(L\)modules). Then we provide some examples and obtain ... 
Labeled Sequent Calculus for Orthologic
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)Orthologic (OL) is nonclassical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic.Sequent calculus is used as a tool for proof in logic and has ... 
Length Neutrosophic Subalgebras of BCK=BCIAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20201230)Given i, j, k ∈ {1,2,3,4}, the notion of (i, j, k)length neutrosophic subalgebras in BCK=BCIalgebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed ... 
Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts
(Wydawnictwo Uniwersytetu Łódzkiego, 20240212)We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the ... 
Linear Abelian Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20231215)A manyvalued modal logic, called linear abelian modal logic \(\rm {\mathbf{LK(A)}}\) is introduced as an extension of the abelian modal logic \(\rm \mathbf{K(A)}\). Abelian modal logic \(\rm \mathbf{K(A)}\) is the minimal ... 
A Logic for Dually Hemimorphic SemiHeyting Algebras and its Axiomatic Extensions
(Wydawnictwo Uniwersytetu Łódzkiego, 20221214)The variety \(\mathbb{DHMSH}\) of dually hemimorphic semiHeyting algebras was introduced in 2011 by the second author as an expansion of semiHeyting algebras by a dual hemimorphism. In this paper, we focus on the variety ... 
Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)In [1] J.Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] ... 
Many Faces of Lattice Tolerances
(Wydawnictwo Uniwersytetu Łódzkiego, 20191231)Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices. 
Mathematical Methods in RegionBased Theories of Space: The Case of Whitehead Points
(Wydawnictwo Uniwersytetu Łódzkiego, 20231204)Regionsbased theories of space aim—among others—to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are ... 
May the SeaBattle Tommorow Not Happen?
(Wydawnictwo Uniwersytetu Łódzkiego, 20200330)This note provides a review of the book 'On the SeaBattle Tomorrow That May Not Happen' by Tomasz Jarmużek. 
The Method of Socratic Proofs Meets Correspondence Analysis
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)The goal of this paper is to propose correspondence analysis as a technique for generating the socalled erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej ... 
Minimal Sequent Calculi for Łukasiewicz’s FinitelyValued Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s nvalued logics [4]. The paper provides an analytical expression of a 2(n−1)place ... 
Modal Boolean Connexive Logics: Semantics and Tableau Approach
(Wydawnictwo Uniwersytetu Łódzkiego, 20191030)In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is nonclassical. ... 
Models of Bounded Arithmetic Theories and Some Related Complexity Questions
(Wydawnictwo Uniwersytetu Łódzkiego, 20220607)In this paper, we study bounded versions of some modeltheoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an ... 
The Modelwise Interpolation Property of Semantic Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 20230421)In this paper we introduce the modelwise interpolation property of a logic that states that whenever \(\models\phi\to\psi\) holds for two formulas \(\phi\) and \(\psi\), then for every model \(\mathfrak{M}\) there is an ... 
A Modified Subformula Property for the Modal Logic S4.2
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)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 cutrule, it is ... 
Module Structure on Effect Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. ... 
Monadic Fragments of Intuitionistic Control Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)We investigate monadic fragments of Intuitionistic Control Logic (ICL), which is obtained from Intuitionistic Propositional Logic (IPL) by extending language of IPL by a constant distinct from intuitionistic constants. In ... 
\(n\)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 ...