Browsing Bulletin of the Section of Logic by Title
Now showing items 48-67 of 195
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Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then ... -
Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as ... -
An Epistemological Study of Theory Change
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-11-09)Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework ... -
Equality Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local ... -
Equivalential Algebras with Conjunction on Dense Elements
(Wydawnictwo Uniwersytetu Łódzkiego, 2022-10-25)We study the variety generated by the three-element equivalential algebra with conjunction on the dense elements. We prove the representation theorem which let us construct the free algebras in this variety. -
Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao. -
Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals
(Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-10)This paper introduces the concept of single-valued neutrosophic hyper \(BCK\)-subalgebras as a generalization and alternative of hyper \(BCK\)-algebras and on any given nonempty set constructs at least one single-valued ... -
Extended MR with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These ... -
Falling Shadow Theory with Applications in Hoops
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-01-20)The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between ... -
First-Order Modal Semantics and Existence Predicate
(Wydawnictwo Uniwersytetu Łódzkiego, 2022-07-11)In the article we study the existence predicate \(\varepsilon\) in the context of semantics for first-order modal logic. For a formula \(\varphi\) we define \(\varphi^{\varepsilon}\) - the so called existence relativization. ... -
Formal Methods and Science in Philosophy: Introduction to the Special Issue
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-06-30)Introduction to the Special Issue. -
Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 4 of a De ... -
Four-Valued Logics BD and DM4: Expansions
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by ... -
Fractional-Valued Modal Logic and Soft Bilateralism
(Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-16)In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) ... -
Free Modal Pseudocomplemented De Morgan Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica ... -
Free Spectra of Equivalential Algebras with Conjunction on Dense Elements
(Wydawnictwo Uniwersytetu Łódzkiego, 2024-05-20)We construct free algebras in the variety generated by the equivalential algebra with conjunction on dense elements and compute the formula for the free spectrum of this variety. Moreover, we describe the decomposition of ... -
From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the ... -
From Intuitionism to Brouwer's Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication ... -
Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that ... -
Functional Completeness in CPL via Correspondence Analysis
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only ...