Browsing Bulletin of the Section of Logic by Title
Now showing items 1938 of 189

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 ... 
Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl
(Wydawnictwo Uniwersytetu Łódzkiego, 20200630)Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a ... 
Complex Fuzzy Sets with Application in BCK/BCIAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20191030)As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCIalgebras. ... 
Compounding Objects
(Wydawnictwo Uniwersytetu Łódzkiego, 20200630)We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which ... 
Computersupported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument
(Wydawnictwo Uniwersytetu Łódzkiego, 20200630)Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument ... 
Constructing a Hoop Using Rough Filters
(Wydawnictwo Uniwersytetu Łódzkiego, 20220909)When it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, ... 
Core Type Theory
(Wydawnictwo Uniwersytetu Łódzkiego, 20230816)Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the ...