Wyświetlanie pozycji 1-12 z 12

    • Axiomatization of a Basic Logic of Logical Bilattices 

      Takano, Mitio (Wydawnictwo Uniwersytetu Łódzkiego, 2016)
      A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices.
    • Cut Elimination for Extended Sequent Calculi 

      Martini, Simone; Masini, Andrea; Zorzi, Margherita (Wydawnictwo Uniwersytetu Łódzkiego, 2023-09-25)
      We present a syntactical cut-elimination proof for an extended sequent calculus covering the classical modal logics in the \(\mathsf{K}\), \(\mathsf{D}\), \(\mathsf{T}\), \(\mathsf{K4}\), \(\mathsf{D4}\) and \(\mathsf{S4}\) ...
    • Functional Completeness in CPL via Correspondence Analysis 

      Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi; Jukiewicz, Marcin (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only ...
    • The Method of Socratic Proofs Meets Correspondence Analysis 

      Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej ...
    • Minimal Sequent Calculi for Łukasiewicz’s Finitely-Valued Logics 

      Pynko, Alexej P. (Wydawnictwo Uniwersytetu Łódzkiego, 2015)
      The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place ...
    • A Modified Subformula Property for the Modal Logic S4.2 

      Takano, Mitio (Wydawnictwo Uniwersytetu Łódzkiego, 2019)
      The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is ...
    • New Modification of the Subformula Property for a Modal Logic 

      Takano, Mitio (Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)
      A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a ...
    • 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 ...
    • Rule-Generation Theorem and its Applications 

      Indrzejczak, Andrzej ORCID (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 ...
    • 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 ...
    • Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus 

      Indrzejczak, Andrzej ORCID (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 ...
    • A Useful Four-Valued Extension of the Temporal Logic KtT4 

      Degauquier, Vincent (Wydawnictwo Uniwersytetu Łódzkiego, 2018)
      The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the ...