Browsing Bulletin of the Section of Logic by Title
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Elementary Proof of Strong Normalization for Atomic F
(Wydawnictwo Uniwersytetu Łódzkiego, 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 Fₐₜ (a predicative restriction of Girard’s system F). 
Empirical Negation, Conegation and Contraposition Rule I: Semantical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as conegation, corresponds to different logics under different semantics. We then ... 
Empirical Negation, CoNegation and the Contraposition Rule II: ProofTheoretical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 20201230)We continue the investigation of the first paper where we studied logics with various negations including empirical negation and conegation. We established how such logics can be treated uniformly with R. Sylvan's CCω as ... 
An Epistemological Study of Theory Change
(Wydawnictwo Uniwersytetu Łódzkiego, 20211109)Belief Revision is a wellestablished 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, 20201104)In this paper, we introduce and study a corresponding logic to equalityalgebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equalityalgebras and local ... 
Equivalential Algebras with Conjunction on Dense Elements
(Wydawnictwo Uniwersytetu Łódzkiego, 20221025)We study the variety generated by the threeelement 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 BCKIdeal Based on SingleValued Neutrosophic Hyper BCKIdeals
(Wydawnictwo Uniwersytetu Łódzkiego, 20230810)This paper introduces the concept of singlevalued neutrosophic hyper \(BCK\)subalgebras as a generalization and alternative of hyper \(BCK\)algebras and on any given nonempty set constructs at least one singlevalued ... 
Extended MR with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena
(Wydawnictwo Uniwersytetu Łódzkiego, 20210630)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, 20210120)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 ... 
FirstOrder Modal Semantics and Existence Predicate
(Wydawnictwo Uniwersytetu Łódzkiego, 20220711)In the article we study the existence predicate \(\varepsilon\) in the context of semantics for firstorder 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, 20200630)Introduction to the Special Issue. 
Fourvalued expansions of DunnBelnap's logic (I): Basic characterizations
(Wydawnictwo Uniwersytetu Łódzkiego, 20201230)Basic results of the paper are that any fourvalued expansion L4 of DunnBelnap'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 ... 
FourValued Logics BD and DM4: Expansions
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)The paper discusses functional properties of some fourvalued logics which are the expansions of fourvalued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by ... 
FractionalValued Modal Logic and Soft Bilateralism
(Wydawnictwo Uniwersytetu Łódzkiego, 20230816)In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of prooftheoretic 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 mpMalgebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica ... 
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 rootfirst translation. The other direction, instead, is tricky, because of the ... 
From Intuitionism to Brouwer's Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20201230)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 ...