Browsing Bulletin of the Section of Logic by Title
Now showing items 143162 of 189

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 ... 
Simple Decision Procedure for S5 in Standard CutFree Sequent Calculus
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)In the paper a decision procedure for S5 is presented which uses a cutfree sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to ... 
Simple Logics for Basic Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)An MValgebra is an algebra (A, ⊕, ¬, 0), where (A, ⊕, 0) is a commutative monoid and ¬ is an idempotent operation on A satisfying also some additional axioms. Basic algebras are similar algebras that can roughly be ... 
Soju Filters in Hoop Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20201230)The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju subhoop, a soju filter and an implicative soju filter are discussed. Conditions ... 
Some Algebraic and Algorithmic Problems in Acoustocerebrography
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human ... 
Some Logics in the Vicinity of Interpretability Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 20231122)In this paper we shall define semantically some families of propositional modal logics related to the interpretability logic \(\mathbf{IL}\). We will introduce the logics \(\mathbf{BIL}\) and \(\mathbf{BIL}^{+}\) in the ... 
Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2017)We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the ... 
A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB
(Wydawnictwo Uniwersytetu Łódzkiego, 20211109)In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf ... 
Stabilizers on \(L\)algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20231120)The main goal of this paper is to introduce the notion of stabilizers in \(L\)algebras and develop stabilizer theory in \(L\)algebras. In this paper, we introduced the notions of left and right stabilizers and investigated ... 
Structural Rules in Natural Deduction with Alternatives
(Wydawnictwo Uniwersytetu Łódzkiego, 20230625)Natural deduction with alternatives extends Gentzen–Prawitzstyle natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, singleconclusion ... 
SUPHesitant Fuzzy Interior Ideals in \(\Gamma\)Semigroups
(Wydawnictwo Uniwersytetu Łódzkiego, 20240424)In this paper, we defined the concept \(\mathcal{SUP}\)hesitant fuzzy interior ideals in \(\Gamma\)semigroups, which is generalized of hesitant fuzzy interior ideals in \(\Gamma\)semigroups. Additionally, we study ...