Bulletin of the Section of Logic: Recent submissions

Now showing items 21-40 of 201

    • 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 ...

    • On Paracomplete Versions of Jaśkowski's Discussive Logic 

      Mruczek-Nasieniewska, Krystyna; Petrukhin, Yaroslav; Shangin, Vasily (Wydawnictwo Uniwersytetu Łódzkiego, 2024-01-04)
      Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the ...

    • Linear Abelian Modal Logic 

      Mohammadi, Hamzeh (Wydawnictwo Uniwersytetu Łódzkiego, 2023-12-15)
      A many-valued modal logic, called linear abelian modal logic \(\rm {\mathbf{LK(A)}}\) is introduced as an extension of the abelian modal logic \(\rm \mathbf{K(A)}\). Abelian modal logic \(\rm \mathbf{K(A)}\) is the minimal ...

    • The Cardinal Squaring Principle and an Alternative Axiomatization of NFU 

      Adlešić, Tin; Čačić, Vedran (Wydawnictwo Uniwersytetu Łódzkiego, 2023-09-28)
      In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal ...

    • A Category of Ordered Algebras Equivalent to the Category of Multialgebras 

      Coniglio, Marcelo Esteban; de Toledo, Guilherme Vicentin (Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-16)
      It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) taking a set to its power-set and, conversely, a complete, atomic Boolean algebra to its set of atomic ...

    • 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 \(\mathsf{S4}\) ...

    • On Implicative and Positive Implicative GE Algebras 

      Walendziak, Andrzej (Wydawnictwo Uniwersytetu Łódzkiego, 2023-09-25)
      GE algebras (generalized exchange algebras), transitive GE algebras (tGE algebras, for short) and aGE algebras (that is, GE algebrasverifying the antisymmetry) are a generalization of Hilbert algebras. Here some properties ...

    • Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals 

      Hamidi , Mohammad (Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-10)
      This paper introduces the concept of single-valued neutrosophic hyper \(BCK\)-subalgebras as a generalization and alternative of hyper \(BCK\)-algebras and on any given nonempty set constructs at least one single-valued ...

    • Fundamental Relation on HvBE-Algebras 

      Iranmanesh, Farzad; Ghadiri, Mansour; Borumand Saeid, Arsham (Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-09)
      In this paper, we are going to introduce a fundamental relation on \(H_{v}BE\)-algebra and investigate some of properties, also construct new \((H_{v})BE\)-algebras via this relation. We show that quotient of any ...

    • Harmony and Normalisation in Bilateral Logic 

      del Valle-Inclan, Pedro (Wydawnictwo Uniwersytetu Łódzkiego, 2023-07-18)
      In a recent paper del Valle-Inclan and Schlöder argue that bilateral calculi call for their own notion of proof-theoretic harmony, distinct from the usual (or ‘unilateral’) ones. They then put forward a specifically bilateral ...

    • Bilateral Rules as Complex Rules 

      Ceragioli, Leonardo (Wydawnictwo Uniwersytetu Łódzkiego, 2023-07-18)
      Proof-theoretic semantics is an inferentialist theory of meaning originally developed in a unilateral framework. Its extension to bilateral systems opens both opportunities and problems. The problems are caused especially ...

    • Supposition: A Problem for Bilateralism 

      Kürbis, Nils (Wydawnictwo Uniwersytetu Łódzkiego, 2023-07-18)
      In bilateral logic formulas are signed by + and –, indicating the speech acts assertion and denial. I argue that making an assumption is also speech act. Speech acts cannot be embedded within other speech acts. Hence we ...

    • Fractional-Valued Modal Logic and Soft Bilateralism 

      Piazza, Mario; Pulcini, Gabriele; Tesi, Matteo (Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-16)
      In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) ...

    • Introduction: Bilateralism and Proof-Theoretic Semantics (Part II) 

      Ayhan, Sara (Wydawnictwo Uniwersytetu Łódzkiego, 2023-09-30)

    • Definite Formulae, Negation-as-Failure, and the Base-Extension Semantics of Intuitionistic Propositional Logic 

      Gheorghiu, Alexander V.; Pym, David J. (Wydawnictwo Uniwersytetu Łódzkiego, 2023-07-18)
      Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension ...

    • On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\) 

      Ayhan, Sara; Wansing, Heinrich (Wydawnictwo Uniwersytetu Łódzkiego, 2023-07-18)
      We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus \(\mathtt{SC2Int}\) for the bi-intuitionistic logic \(\mathtt{2Int}\). A ...

    • Core Type Theory 

      van Dijk, Emma; Ripley, David; Gutierrez, Julian (Wydawnictwo Uniwersytetu Łódzkiego, 2023-08-16)
      Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the ...

    • 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 ...

    • Introduction: Bilateralism and Proof-Theoretic Semantics (Part I) 

      Ayhan, Sara (Wydawnictwo Uniwersytetu Łódzkiego, 2023-06-30)

    • The Weak Variable Sharing Property 

      Øgaard, Tore Fjetland (Wydawnictwo Uniwersytetu Łódzkiego, 2023-04-21)
      An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all ...