Browsing Bulletin of the Section of Logic by Title

Now showing items 144-163 of 189

    • Reasoning about Social Phenomena 

      Jarmużek, Tomasz; Ju, Fengkui; Kulicki, Piotr; Liao, Beishui (Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)

    • Roughness of Filters in Equality Algebras 

      Rezaei, Gholam Reza; Borzooei, Rajab Ali; Aaly Kologani, Mona; Jun, Young Bae (Wydawnictwo Uniwersytetu Łódzkiego, 2023-01-25)
      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 ...

    • Rule-Generation Theorem and its Applications 

      Indrzejczak, Andrzej (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 

      Yazaki, Daishi (Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)
      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 ...

    • Semi-Heyting Algebras and Identities of Associative Type 

      Cornejo, Juan M.; Sankappanavar, Hanamantagouda P. (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting 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 Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics 

      Tomova, Natalya (Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-13)
      In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect ...

    • Sequent Calculi for Orthologic with Strict Implication 

      Kawano, Tomoaki (Wydawnictwo Uniwersytetu Łódzkiego, 2021-11-09)
      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 

      Płaczek, Paweł (Wydawnictwo Uniwersytetu Łódzkiego, 2024-04-24)
      Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is Multiplicative-Additive Linear Logic (MALL), which forms the exponential-free ...

    • A Sequent Systems without Improper Derivations 

      Sasaki, Katsumi (Wydawnictwo Uniwersytetu Łódzkiego, 2021-10-14)
      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 Cut-Free Sequent Calculus 

      Indrzejczak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      In the paper a decision procedure for S5 is presented which uses a cut-free 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 

      Cı̅rulis, Ja̅nis (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      An MV-algebra 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 

      Borzooei, Rajab Ali; Rezaei, Gholam Reza; Kologhani, Mona Aaly; Jun, Young Bae (Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
      The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions ...

    • Some Algebraic and Algorithmic Problems in Acoustocerebrography 

      Kolany, Adam; Wrobel, Miroslaw (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 

      Celani, Sergio A. (Wydawnictwo Uniwersytetu Łódzkiego, 2023-11-22)
      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 

      Suzuki, Nobu-Yuki (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 

      Inoue, Takao (Wydawnictwo Uniwersytetu Łódzkiego, 2021-11-09)
      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 

      Rezaei, Gholam Reza; Aaly Kologani, Mona (Wydawnictwo Uniwersytetu Łódzkiego, 2023-11-20)
      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 

      Restall, Greg (Wydawnictwo Uniwersytetu Łódzkiego, 2023-06-25)
      Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion ...

    • SUP-Hesitant Fuzzy Interior Ideals in \(\Gamma\)-Semigroups 

      Khamrot, Pannawit; Gaketem, Thiti (Wydawnictwo Uniwersytetu Łódzkiego, 2024-04-24)
      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 ...

    • Super-Strict Implications 

      Gherardi, Guido; Orlandelli, Eugenio (Wydawnictwo Uniwersytetu Łódzkiego, 2021-01-20)
      This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those ...