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    Wyświetlanie 1-11 z 11
    Tytuł:
    Monadic Fragments of Intuitionistic Control Logic
    Autorzy:
    Glenszczyk, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/749902.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Intuitionistic Control Logic
    Intuitionistic Logic
    Combining Logic
    Control Operators
    Opis:
    We investigate monadic fragments of Intuitionistic Control Logic (ICL), which is obtained from Intuitionistic Propositional Logic (IPL) by extending language of IPL by a constant distinct from intuitionistic constants. In particular we present the complete description of purely negational fragment and show that most of monadic fragments are finite.
    Źródło:
    Bulletin of the Section of Logic; 2016, 45, 3/4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An Alternative Natural Deduction for the Intuitionistic Propositional Logic
    Autorzy:
    Ilić, Mirjana
    Powiązania:
    https://bibliotekanauki.pl/articles/749978.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    natural deduction
    intuitionistic logic
    Opis:
    A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.
    Źródło:
    Bulletin of the Section of Logic; 2016, 45, 1
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    From Intuitionism to Brouwers Modal Logic
    Autorzy:
    Kostrzycka, Zofia
    Powiązania:
    https://bibliotekanauki.pl/articles/1023286.pdf
    Data publikacji:
    2020-12-30
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    intuitionistic logic
    Kripke frames
    Brouwer's modal logic
    Opis:
    We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.
    Źródło:
    Bulletin of the Section of Logic; 2020, 49, 4; 343-358
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras
    Autorzy:
    Dzik, Wojciech
    Radeleczki, Sándor
    Powiązania:
    https://bibliotekanauki.pl/articles/749994.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    filtering unification
    compatible operation
    intuitionistic logic
    Heyting algebra
    residuated lattice
    Opis:
    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 for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, γ and G operations as well as expansions of some commutative integral residuated lattices with successor operations.
    Źródło:
    Bulletin of the Section of Logic; 2016, 45, 3/4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate
    Autorzy:
    Maffezioli, Paolo
    Orlandelli, Eugenio
    Powiązania:
    https://bibliotekanauki.pl/articles/749910.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    intuitionistic logic
    existence predicate
    sequent calculi
    cut elimination
    interpolation
    Maehara's lemma
    Opis:
    In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and (partly) overcome the failure of interpolation for the implication-free fragment.
    Źródło:
    Bulletin of the Section of Logic; 2019, 48, 2; 137-158
    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 Investigation into Intuitionistic Logic with Identity
    Autorzy:
    Chlebowski, Szymon
    Leszczyńska-Jasion, Dorota
    Powiązania:
    https://bibliotekanauki.pl/articles/750046.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Non-Fregean logics
    intuitionistic logic
    admissibility of cut
    propositional identity
    congruence
    Opis:
    We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective.
    Źródło:
    Bulletin of the Section of Logic; 2019, 48, 4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Note on the Intuitionistic Logic of False Belief
    Autorzy:
    Witczak, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/2142756.pdf
    Data publikacji:
    2021-09-01
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Intuitionistic modal logic
    non-normal modal logic
    neighborhood semantics
    Opis:
    In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ is not satisfied in a given world, but we still believe in it (or we think that it should be accepted). Another interpretations are also possible: e.g. that we do not accept $\varphi$ but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is expressed by an adequate form of modal operator $\mathsf{W}$ which is interpreted in relational frames with neighborhoods. We discuss monotonicity of forcing, soundness, completeness and several other issues. Finally, we mention the fact that it is possible to investigate intuitionistic logics of unknown truths.
    Źródło:
    Bulletin of the Section of Logic; 2022, 51, 1; 57-71
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Synonymy in Proof-Theoretic Semantics: The Case of \(\mathtt{2Int}\)
    Autorzy:
    Ayhan, Sara
    Wansing, Heinrich
    Powiązania:
    https://bibliotekanauki.pl/articles/43181589.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    bilateralism
    bi-intuitionistic logic \(\mathtt{2Int}\)
    cut-elimination
    identity of derivations
    synonymy
    Opis:
    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 distinctive feature of \(\mathtt{SC2Int}\) is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of \(\mathtt{SC2Int}\), in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated through two different negation connectives, the well-known implies-falsity negation and the less well-known coimplies-truth negation of \(\mathtt{2Int}\). By assuming that the interaction rules have no impact on the identity of derivations, the concept of inherited identity between derivations in \(\mathtt{SC2Int}\) is introduced and the notions of positive and negative synonymy of formulas are defined. Several examples are given of distinct formulas that are either positively or negatively synonymous. It is conjectured that the two conditions cannot be satisfied simultaneously.
    Źródło:
    Bulletin of the Section of Logic; 2023, 52, 2; 187-237
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic
    Autorzy:
    Witczak, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/749992.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    intuitionistic modal logic
    neighbourhood semantics
    topological semantics
    Kripke frames
    soundness and completeness
    Opis:
    We present three examples of topological semantics for intuitionistic modal logic with one modal operator □. We show that it is possible to treat neighborhood models, introduced earlier, as topological or multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multitopological spaces into the neighborhood structures.
    Źródło:
    Bulletin of the Section of Logic; 2019, 48, 3; 187-205
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Logic for Dually Hemimorphic Semi-Heyting Algebras and its Axiomatic Extensions
    Autorzy:
    Cornejo, Juan Manuel
    Sankappanavar, Hanamantagouda P.
    Powiązania:
    https://bibliotekanauki.pl/articles/43189647.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    semi-intuitionistic logic
    dually hemimorphic semi-Heyting logic
    dually quasi-De Morgan semi-Heyting logic
    De Morgan semi-Heyting logic
    dually pseudocomplemented semi-Heyting logic
    regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1
    implicative logic
    equivalent algebraic semantics
    algebraizable logic
    De Morgan Gödel logic
    dually pseudocomplemented Gödel logic
    Moisil's logic
    3-valued Łukasiewicz logic
    Opis:
    The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras.
    Źródło:
    Bulletin of the Section of Logic; 2022, 51, 4; 555-645
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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