Browsing Bulletin of the Section of Logic by Title
Now showing items 120 of 112

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 ... 
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. 
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 ... 
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 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 ... 
Categorical Abstract Algebraic Logic: Referential πInstitutions
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of ... 
Categorical Abstract Algebraic Logic: PseudoReferential Matrix System Semantics
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)This work adapts techniques and results first developed by Malinowski and by Marek in the context of referential semantics of sentential logics to the context of logics formalized as πinstitutions. More precisely, the ... 
Categorical Abstract Logic: Hidden MultiSorted Logics as MultiTerm Institutions
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Babenyshev and Martins proved that two hidden multisorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with ... 
Characterization of Birkhoff’s Conditions by Means of CoverPreserving and Partially CoverPreserving Sublattices
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)In the paper we investigate Birkhoff’s conditions (Bi) and (Bi*). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi*)) if and only if L is a 4cell lattice not containing a coverpreserving ... 
Closure Operators on Complete Almost Distributive LatticesIII
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meetirreducible element ... 
Commutative Energetic Subsets of BCKAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The notions of a Cenergetic subset and (anti) permeable Cvalue in BCKalgebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable Cvalue are provided. ... 
A comparison of two systems of pointfree topology
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)This is a spinoff paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s pointfree topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was ...