Browsing Bulletin of the Section of Logic by Title
Now showing items 133152 of 189

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. ... 
Positive Implicative Soju Ideals in BCKAlgebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)The notion of positive implicative soju ideal in BCKalgebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations ... 
A poststyle proof of completeness theorem for symmetric relatedness Logic S
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a ... 
Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that ... 
Professor Grzegorz Malinowski in Honorem
(Wydawnictwo Uniwersytetu Łódzkiego, 2017) 
Proof Compression and NP Versus PSPACE II
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)We upgrade [3] to a complete proof of the conjecture NP = PSPACE that is known as one of the fundamental open problems in the mathematical theory of computational complexity; this proof is based on [2]. Since minimal ... 
Proof Compression and NP Versus PSPACE II: Addendum
(Wydawnictwo Uniwersytetu Łódzkiego, 20220107)In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cutfree sequent calculus for minimal logic (HSC) with the horizontal compressing in the corresponding ... 
PseudoBCH Semilattices
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)In this paper we study pseudoBCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudoBCH joinsemilattices, pseudoBCH meetsemilattices and pseudoBCH lattices, ... 
Quasiorders, Tolerance Relations and Corresponding “Partitions”
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based ... 
Reasoning about Social Phenomena
(Wydawnictwo Uniwersytetu Łódzkiego, 20210630) 
Roughness of Filters in Equality Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20230125)Rough set theory is an excellent mathematical tool for the analysis of a vague description of actions in decision problems. Now, in this paper by considering the notion of an equality algebra, the notion of the lower and ... 
RuleGeneration Theorem and its Applications
(Wydawnictwo Uniwersytetu Łódzkiego, 2018)In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical ... 
Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3
(Wydawnictwo Uniwersytetu Łódzkiego, 20191231)The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and ... 
SemiHeyting Algebras and Identities of Associative Type
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semiHeyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. SH denotes ... 
A Semilattice of Fourvalued Literalparaconsistentparacomplete Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 20201113)In this paper, we consider the class of fourvalued literalparaconsistentparacomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10element upper semilattice with respect ... 
Sequent Calculi for Orthologic with Strict Implication
(Wydawnictwo Uniwersytetu Łódzkiego, 20211109)In this study, new sequent calculi for a minimal quantum logic (\(\bf MQL\)) are discussed that involve an implication. The sequent calculus \(\bf GO\) for \(\bf MQL\) was established by Nishimura, and it is complete with ... 
Sequent Systems for Consequence Relations of Cyclic Linear Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 20240424)Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is MultiplicativeAdditive Linear Logic (MALL), which forms the exponentialfree ... 
A Sequent Systems without Improper Derivations
(Wydawnictwo Uniwersytetu Łódzkiego, 20211014)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, and others ...