Browsing Bulletin of the Section of Logic by Title
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Harmony and Normalisation in Bilateral Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20230718)In a recent paper del ValleInclan and Schlöder argue that bilateral calculi call for their own notion of prooftheoretic harmony, distinct from the usual (or ‘unilateral’) ones. They then put forward a specifically bilateral ... 
Identity, Equality, Nameability and Completeness
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the ... 
Identity, equality, nameability and completeness. Part II
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)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 ... 
InfHesitant Fuzzy Ideals in BCK/BCIAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20200330)Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Infhesitant fuzzy subalgebras, Infhesitant fuzzy ideals and Infhesitant fuzzy pideals in BCK/BCIalgebras are ... 
An Inferentially ManyValued TwoDimensional Notion of Entailment
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)Starting from the notions of qentailment and pentailment, a twodimensional notion of entailment is developed with respect to certain generalized qmatrices referred to as Bmatrices. After showing that every purely ... 
The InfiniteValued Łukasiewicz Logic and Probability
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinitevalued Łukasiewicz algebra. The paper also discusses ... 
IntSoft Ideals of Pseudo MVAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)The notion of (implicative) intsoft ideal in a pseudo MValgebra is introduced, and related properties are investigated. Conditions for a soft set to be an intsoft ideal are provided. Characterizations of (implicative) ... 
Interpolation in Normal Extensions of the Brouwer Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic. 
Interpolation Property on Visser's Formal Propositional Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20220920)In this paper by using a modeltheoretic approach, we prove Craig interpolation property for Formal Propositional Logic, FPL, Basic propositional logic, BPL and the uniform leftinterpolation property for FPL. We also ... 
Introduction: Bilateralism and ProofTheoretic Semantics (Part I)
(Wydawnictwo Uniwersytetu Łódzkiego, 20230630) 
Introduction: Bilateralism and ProofTheoretic Semantics (Part II)
(Wydawnictwo Uniwersytetu Łódzkiego, 20230930) 
An Investigation into Intuitionistic Logic with Identity
(Wydawnictwo Uniwersytetu Łódzkiego, 20191231)We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cutelimination theorem. We sketch a constructive interpretation of Suszko’s ... 
Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)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 ... 
Irredundant Decomposition of Algebras into OneDimensional Factors
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)We introduce a notion of dimension of an algebraic lattice and, treating such a lattice as the congruence lattice of an algebra, we introduce the dimension of an algebra, too. We define a starproduct as a special kind of ... 
\(L\)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 ...