Browsing Bulletin of the Section of Logic by Title
Now showing items 1332 of 189

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 ... 
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 ... 
Categorical Dualities for Some Two Categories of Lattices: An Extended Abstract
(Wydawnictwo Uniwersytetu Łódzkiego, 20220802)The categorical dualities presented are: (first) for the category of bialgebraic lattices that belong to the variety generated by the smallest nonmodular lattice with complete (0,1)lattice homomorphisms as morphisms, ... 
A Category of Ordered Algebras Equivalent to the Category of Multialgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20230816)It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) taking a set to its powerset and, conversely, a complete, atomic Boolean algebra to its set of atomic ... 
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 ... 
A Classification of Improper Inference Rules
(Wydawnictwo Uniwersytetu Łódzkiego, 20220623)In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper as opposed to ... 
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 ... 
Common Knowledge, Common Attitudes and Social Reasoning
(Wydawnictwo Uniwersytetu Łódzkiego, 20210630)For as long as there have been theories about common knowledge, they have been exposed to a certain amount of skepticism. Recent more sophisticated arguments question whether agents can acquire common attitudes and whether ... 
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 ... 
Complete Representations and Neat Embeddings
(Wydawnictwo Uniwersytetu Łódzkiego, 20220909)Let \(2<n<\omega\). Then \({\sf CA}_n\) denotes the class of cylindric algebras of dimension \(n\), \({\sf RCA}_n\) denotes the class of representable \(\sf CA_n\)s, \({\sf CRCA}_n\) denotes the class of completely ...