Browsing Bulletin of the Section of Logic by Title
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Omitting Types in Fragments and Extensions of First Order Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20210528)Fix \(2 < n < \omega\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for ... 
On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
(Wydawnictwo Uniwersytetu Łódzkiego, 20210721)Fix a finite ordinal \(n\geq 3\) and let \(\alpha\) be an arbitrary ordinal. Let \(\mathsf{CA}_n\) denote the class of cylindric algebras of dimension \(n\) and \(\sf RA\) denote the class of relation algebras. Let ... 
On Direct Limit Closed Classes of Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Axiomatic classes of algebras of a given type which are closed with respect to direct limits are studied in this paper. 
On GEalgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20200830)Hilbert algebras are important tools for certain investigations in intuitionistic logic and other nonclassical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GEalgebra (generalized ... 
On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames. 
On Homomorphism and Cartesian Products of Intuitionistic Fuzzy PMSsubalgebra of a PMSalgebra
(Wydawnictwo Uniwersytetu Łódzkiego, 20230421)In this paper, we introduce the notion of intuitionistic fuzzy PMSsubalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic ... 
On Implicative and Positive Implicative GE Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20230925)GE algebras (generalized exchange algebras), transitive GE algebras (tGE algebras, for short) and aGE algebras (that is, GE algebrasverifying the antisymmetry) are a generalization of Hilbert algebras. Here some properties ... 
On Injective MVModules
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)In this paper, by considering the notion of MVmodule, which is the structure that naturally correspond to lumodules over lurings, we study injective MVmodules and we investigate some conditions for constructing injective ... 
On interpolation in next (kb.alt(2))
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)We prove that there is infinitely many tabular modal logics extending KB.Alt(2) which have interpolation. 
On Paracomplete Versions of Jaśkowski's Discussive Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20240104)Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the ... 
On Some Applied FirstOrder Theories which Can Be Represented by Definitions
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this ... 
On Synonymy in ProofTheoretic Semantics: The Case of \(\mathtt{2Int}\)
(Wydawnictwo Uniwersytetu Łódzkiego, 20230718)We consider an approach to propositional synonymy in prooftheoretic semantics that is defined with respect to a bilateral G3style sequent calculus \(\mathtt{SC2Int}\) for the biintuitionistic logic \(\mathtt{2Int}\). A ... 
On the Category of EQalgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20210120)In this paper, we studied the category of EQalgebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQalgebras have coequlizers and we calculated coproduct ... 
On the Definability of Leśniewski’s Copula ‘is’ in Some OntologyLike Theories
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)We formulate a certain subtheory of Ishimoto’s [1] quantifierfree fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is ... 
On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only ... 
On Theses without Iterated Modalities of Modal Logics Between C1 and S5. Part 2
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only ... 
OneSided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity
(Wydawnictwo Uniwersytetu Łódzkiego, 20201113)Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a onesided (in fact, leftsided) sequent system for this logic. Here we prove an analogous result for the ... 
A Paradox for the Existence Predicate
(Wydawnictwo Uniwersytetu Łódzkiego, 20220610)In this paper, a paradox is shown to arise in the context of classical logic from prima facie highly plausible assumptions for the existence predicate as applied to definite descriptions. There are several possibilities ... 
PClattices: A Class of Bounded BCKalgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)In this paper, we define the notion of PClattice, as a generalization of finite positive implicative BCKalgebras with condition (S) and bounded commutative BCKalgebras. We investiate some results for Pclattices being ... 
The Phenomenology of SecondLevel Inference: Perfumes in The Deductive Garden
(Wydawnictwo Uniwersytetu Łódzkiego, 20201230)We comment on certain features that secondlevel inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goalsimplification, goalpreservation and premisepreservation. ...