Browsing Bulletin of the Section of Logic by Title
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A 2 SetUp Binary Routley Semantics for Gödelian 3Valued Logic G3 and Its Paraconsistent Counterpart G3\(_\text{Ł}^\leq\)
(Wydawnictwo Uniwersytetu Łódzkiego, 20221014)G3 is Gödelian 3valued logic, G3\(_\text{Ł}^\leq\) is its paraconsistent counterpart and G3\(_\text{Ł}^1\) is a strong extension of G3\(_\text{Ł}^\leq\). The aim of this paper is to endow each one of the logics just ... 
A 2setup RoutleyMeyer Semantics for the 4valued Relevant Logic E4
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The logic BN4 can be considered as the 4valued logic of the relevant conditional and the logic E4, as the 4valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2setup RoutleyMeyer semantics. ... 
A Note on some Characterization of Distributive Lattices of Finite Length
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)Using known facts we give a simple characterization of the distributivity of lattices of finite length. 
A Short and Readable Proof of Cut Elimination for Two FirstOrder Modal Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)A well established technique toward developing the proof theory of a Hilbertstyle modal logic is to introduce a Gentzenstyle equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer ... 
Algebraic Characterization of the Local Craig Interpolation Property
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. ... 
An Alternative Natural Deduction for the Intuitionistic Propositional Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via ... 
An Elementary Proof of Strong Normalization for Atomic F
(Uniwersytet Łódzki. Katedra Logiki i Metodologii Nauk, 2016)We give an elementary proof (in the sense that it is formalizable in Peano arithmetic) of the strong normalization of the atomic polymorphic calculus F_{at} (a predicative restriction of Girard’s system F). 
An Observation Concerning Porte’s Rule in Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent ... 
Analytic NonLabelled ProofSystems for Hybrid Logic: Overview and a couple of striking facts
(Wydawnictwo Uniwersytetu Łódzkiego, 20220107)This paper is about nonlabelled proofsystems for hybrid logic, that is, proofsystems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proofsystems, focusing on analytic ... 
Applications of Algebra in Logic and Computer Science – the Past and the Future
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twentythird edition will be held in March, 2019. At the end we outline some plans for the future. 
An Arithmetically Complete Predicate Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20210823)This paper investigates a firstorder extension of GL called \(\textup{ML}^3\). We outline briefly the history that led to \(\textup{ML}^3\), its key properties and some of its toolbox: the \emph{conservation theorem}, its ... 
Axiomatization of a Basic Logic of Logical Bilattices
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)A sequential axiomatization is given for the 16valued logic that has been proposed by ShramkoWansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices. 
Balmost distributive fuzzy lattice
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)The paper introduces the concept of BAlmost distributive fuzzy lattice (BADFL) in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a BADFL are investigated. We also ... 
Basic FourValued Systems of Cyclic Negations
(Wydawnictwo Uniwersytetu Łódzkiego, 20221025)We consider an example of four valued semantics partially inspired by quantum computations and negationlike operations occurred therein. In particular we consider a representation of so called square root of negation ... 
Bayesian Propositional Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: ≈w , where w is a probability function on a Boolean ... 
A Benchmark Similarity Measures for Fermatean Fuzzy Sets
(Wydawnictwo Uniwersytetu Łódzkiego, 20220608)In this paper, we utilized triangular conorms (Snorm). The essence of using Snorm is that the similarity order does not change using different norms. In fact, we are investigating for a new conception for calculating the ... 
Bilateral Rules as Complex Rules
(Wydawnictwo Uniwersytetu Łódzkiego, 20230718)Prooftheoretic semantics is an inferentialist theory of meaning originally developed in a unilateral framework. Its extension to bilateral systems opens both opportunities and problems. The problems are caused especially ... 
A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic ... 
Cantor on Infinitesimals. Historical and Modern Perspective
(Wydawnictwo Uniwersytetu Łódzkiego, 20200630)In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that ... 
The Cardinal Squaring Principle and an Alternative Axiomatization of NFU
(Wydawnictwo Uniwersytetu Łódzkiego, 20230928)In this paper, we rigorously prove the existence of typelevel ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal ...