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Tytuł:
On Paracomplete Versions of Jaśkowskis Discussive Logic
Autorzy:
Mruczek-Nasieniewska, Krystyna
Petrukhin, Yaroslav
Shangin, Vasily
Powiązania:
https://bibliotekanauki.pl/articles/43183714.pdf
Data publikacji:
2024
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
discussive logic
discursive logic
modal logic
paracomplete logic
paraconsistent logic
Opis:
Jaśkowski's discussive (discursive) logic \( \mathbf{D_2} \) 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 modal logic \( \mathbf{ S5 } \) via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic \( \mathbf{ D_2^p } \).
Źródło:
Bulletin of the Section of Logic; 2024, 53, 1; 29-61
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
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:
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:
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:
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
Tytuł:
A Note on Ciuciura’s mbC1
Autorzy:
Omori, Hitoshi
Powiązania:
https://bibliotekanauki.pl/articles/749998.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
paraconsistent logic
non-deterministic semantics contra-classical logic
Opis:
This note offers a non-deterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and (strong) completeness results with respect to the Hilbert-style proof system. Moreover, based on the new semantics, we briefly discuss an unexplored variant of mbC1 which has a contra-classical flavor.
Źródło:
Bulletin of the Section of Logic; 2019, 48, 3; 161-171
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics
Autorzy:
Gao, Feng
Tourlakis, George
Powiązania:
https://bibliotekanauki.pl/articles/749884.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Modal logic
GL
QGL
first-order logic
proof theory
cut elimination
cut admissibility
provability logic
Opis:
A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer the metatheoretical results to the original logic (e.g., [1, 6, 8, 18, 10, 12]). In the first-order modal case, on one hand we know that the Gentzenisation of the straightforward first-order extension of GL, the logic QGL, admits no cut elimination (if the rule is included as primitive; or, if not included, then the rule is not admissible [1]). On the other hand the (cut-free) Gentzenisations of the first-order modal logics M3 and ML3 of [10, 12] do have cut as an admissible rule. The syntactic cut admissibility proof given in [18] for the Gentzenisation of the propositional provability logic GL is extremely complex, and it was the basis of the proofs of cut admissibility of the Gentzenisations of M3 and ML3, where the presence of quantifiers and quantifier rules added to the complexity and length of the proof. A recent proof of cut admissibility in a cut-free Gentzenisation of GL is given in [5] and is quite short and easy to read. We adapt it here to revisit the proofs for the cases of M3 and ML3, resulting to similarly short and easy to read proofs, only slightly complicated by the presence of quantification and its relevant rules.
Źródło:
Bulletin of the Section of Logic; 2015, 44, 3-4
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:
Deontic Paradoxes and Tableau System for Kalinowski’s Deontic Logic K1
Autorzy:
Ciuciura, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/750004.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
deontic logic
K1
Kalinowski’s logic
paradoxes
tableaux
Opis:
In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.
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
Tytuł:
Extended MR with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena
Autorzy:
Parol, Aleksander
Pietrowicz, Krzysztof
Szalacha-Jarmużek, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/1812204.pdf
Data publikacji:
2021-06-30
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
logic for social sciences
positional logic
realisation operator
social phenomena
Opis:
In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These expressions allow, inter alia, to consider different points of view of social entities (humanistic coefficient). In the article, we perform a metalogical analysis of this logic. Finally, we present some simple examples of its application.
Źródło:
Bulletin of the Section of Logic; 2021, 50, 2; 205-227
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nilpotent Minimum Logic NM and Pretabularity
Autorzy:
Yang, Eunsuk
Powiązania:
https://bibliotekanauki.pl/articles/750006.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
pretabularity
nilpotent minimum logic
algebraic semantics
fuzzy logic
finite model property
Opis:
This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM-. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.  
Źródło:
Bulletin of the Section of Logic; 2020, 49, 1
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
Applications of Algebra in Logic and Computer Science – the Past and the Future
Autorzy:
Grygiel, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/749898.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
conference
algebra
logic
applications
Opis:
We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twenty-third edition will be held in March, 2019. At the end we outline some plans for the future.
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
Wyświetlanie 1-15 z 80

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