Browsing Bulletin of the Section of Logic by Title

Now showing items 133-152 of 189

    • A Paradox for the Existence Predicate 

      Meixner, Uwe (Wydawnictwo Uniwersytetu Łódzkiego, 2022-06-10)
      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 ...

    • PC-lattices: A Class of Bounded BCK-algebras 

      Shoar, Sadegh Khosravi; Borzooei, Rajab Ali; Moradian, R.; Radfar, Atefe (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being ...

    • The Phenomenology of Second-Level Inference: Perfumes in The Deductive Garden 

      Makinson, David (Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)
      We comment on certain features that second-level inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goal-simplification, goal-preservation and premise-preservation. ...

    • Positive Implicative Soju Ideals in BCK-Algebras 

      Xin, Xiao Long; Borzooei, Rajab Ali; Jun, Young Bae (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations ...

    • A post-style proof of completeness theorem for symmetric relatedness Logic S 

      Klonowski, Mateusz (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 

      Dzik, Wojciech; Radeleczki, Sándor (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 

      Indrzejczak, Andrzej; Ciuciura, Janusz (Wydawnictwo Uniwersytetu Łódzkiego, 2017)

    • Proof Compression and NP Versus PSPACE II 

      Gordeev, Lew; Haeusler, Edward Hermann (Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)
      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 

      Gordeev, Lew; Haeusler, Edward Hermann (Wydawnictwo Uniwersytetu Łódzkiego, 2022-01-07)
      In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic (HSC) with the horizontal compressing in the corresponding ...

    • Pseudo-BCH Semilattices 

      Walendziak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, ...

    • Quasiorders, Tolerance Relations and Corresponding “Partitions” 

      Nowak, Marek (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 

      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 ...