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    Wyświetlanie 1-7 z 7
    Tytuł:
    A Variant of Material Connexive Logic
    Autorzy:
    Belikov, Alexander
    Zaitsev, Dmitry
    Powiązania:
    https://bibliotekanauki.pl/articles/2142753.pdf
    Data publikacji:
    2021-11-09
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    many-valued logics
    connexive logic
    four-valued logic MC
    informal reasoning
    Opis:
    The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius’ (and thus, Aristotle’s) Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.
    Źródło:
    Bulletin of the Section of Logic; 2022, 51, 2; 227-242
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Linear Abelian Modal Logic
    Autorzy:
    Mohammadi, Hamzeh
    Powiązania:
    https://bibliotekanauki.pl/articles/43184005.pdf
    Data publikacji:
    2024
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    many-valued logic
    modal logic
    abelian logic
    hypersequent calculus
    cut-elimination
    Opis:
    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 modal extension of the logic of lattice-ordered abelian groups. The logic \(\rm \mathbf{LK(A)}\) is axiomatized by extending \(\rm \mathbf{K(A)}\) with the modal axiom schemas \(\Box(\varphi\vee\psi)\rightarrow(\Box\varphi\vee\Box\psi)\) and \((\Box\varphi\wedge\Box\psi)\rightarrow\Box(\varphi\wedge\psi)\). Completeness theorem with respect to algebraic semantics and a hypersequent calculus admitting cut-elimination are established. Finally, the correspondence between hypersequent calculi and axiomatization is investigated.
    Źródło:
    Bulletin of the Section of Logic; 2024, 53, 1; 1-28
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equality Logic
    Autorzy:
    Ghorbani, Shokoofeh
    Powiązania:
    https://bibliotekanauki.pl/articles/1023179.pdf
    Data publikacji:
    2020-11-04
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    many-valued logic
    equality logic
    completness
    prelinear equality∆-algebra
    prelinear equality∆ logic
    Opis:
    In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive systems of equality∆-algebras. In particular, we prove that every prelinear equality ∆-algebra is a subdirect product of linearly ordered equality∆-algebras. Finally, we construct prelinear equality ∆ logic and prove the soundness and strong completeness of this logic respect to prelinear equality∆-algebras.
    Źródło:
    Bulletin of the Section of Logic; 2020, 49, 3; 291-324
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional-Valued Modal Logic and Soft Bilateralism
    Autorzy:
    Piazza, Mario
    Pulcini, Gabriele
    Tesi, Matteo
    Powiązania:
    https://bibliotekanauki.pl/articles/43181839.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    modal logic
    general proof theory (including proof-theoretic semantics)
    many-valued logics
    Opis:
    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 \([0,1]\) of rational numbers [14]. In this paper, after clarifying our conception of bilateralism – dubbed “soft bilateralism” – we generalize the fractional method to encompass extensions and weakenings of \(\mathbf{K}\). Specifically, we introduce well-behaved hypersequent calculi for the deontic logic \(\mathbf{D}\) and the non-normal modal logics \(\mathbf{E}\) and \(\mathbf{M}\) and thoroughly investigate their structural properties.
    Źródło:
    Bulletin of the Section of Logic; 2023, 52, 3; 275-299
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4
    Autorzy:
    Robles, Gemma
    López, Sandra M.
    Blanco, José M.
    Recio, Marcos M.
    Paradela, Jesús R.
    Powiązania:
    https://bibliotekanauki.pl/articles/749920.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Relevant logics
    many-valued logics
    4-valued logics
    2-set-up Routley-Meyer semantics
    Opis:
    The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.
    Źródło:
    Bulletin of the Section of Logic; 2016, 45, 2
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Useful Four-Valued Extension of the Temporal Logic KtT4
    Autorzy:
    Degauquier, Vincent
    Powiązania:
    https://bibliotekanauki.pl/articles/749896.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    temporal logic
    many-valued logic
    bi-intuitionistic logic
    paraconsistent logic
    sequent calculus
    duality
    cut-redundancy
    Opis:
    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 axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial and paraconsistent logics.
    Źródło:
    Bulletin of the Section of Logic; 2018, 47, 1
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An Inferentially Many-Valued Two-Dimensional Notion of Entailment
    Autorzy:
    Blasio, Carolina
    Marcos, João
    Wansing, Heinrich
    Powiązania:
    https://bibliotekanauki.pl/articles/750014.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Inferential many-valuedness
    two-dimensional entailment
    B-matrices
    B-consequence relations
    monotonic consequence relations
    q-entailment
    p-entailment
    Suszko Reduction
    Opis:
    Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko’s Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued.
    Źródło:
    Bulletin of the Section of Logic; 2017, 46, 3/4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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