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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:
Siła i słabość logik modalnych
The Strengths and Weaknesses of Modal Logics
Autorzy:
Czakon, Marcin
Powiązania:
https://bibliotekanauki.pl/articles/909495.pdf
Data publikacji:
2020-03-31
Wydawca:
Uniwersytet Warszawski. Wydział Filozofii
Tematy:
modal logic
temporal logic
epistemic logic
Opis:
This is a review of the book Jedność i wielość logik modalnych (The Unity and Diversity of Modal Logics) edited by Marcin Tkaczyk. The book contains discussions of the most recent results of contemporary modal logic, focusing on regular modal logics, epistemic logic, and temporal logic. The book comprises four chapter, each of which deals with selected formal-logical and philosophical problems associated with modal logic.
Źródło:
Filozofia Nauki; 2020, 28, 1; 125-132
1230-6894
2657-5868
Pojawia się w:
Filozofia Nauki
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:
Neighbourhood Semantics for Graded Modal Logic
Autorzy:
Chen, Jinsheng
van Ditmarsch, Hans
Greco, Giuseppe
Tzimoulis, Apostolos
Powiązania:
https://bibliotekanauki.pl/articles/2033856.pdf
Data publikacji:
2021-07-14
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Graded modal logic
neighbourhood frames
bisimulation
Opis:
We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.
Źródło:
Bulletin of the Section of Logic; 2021, 50, 3; 373-395
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Najkrótsze aksjomaty modalnej logiki Łukasiewicza
The Shortest Axioms of Łukasiewicz’s Modal Logic
Autorzy:
Dywan, Zdzisław
Powiązania:
https://bibliotekanauki.pl/articles/488405.pdf
Data publikacji:
2016
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
aksjomatyzacja
logika modalna
axiomatization
modal logic
Opis:
Pokazujemy, że formuła CLpEqLq aksjomatyzuje logikę modalną Łukasiewicza i nie istnieje krótszy aksjomat dla tej logiki.
We show that the formula CLpEqLq axiomatizes Łukasiewicz’s modal logic and that there exists no shorter axiom for it.
Źródło:
Roczniki Filozoficzne; 2016, 64, 2; 5-9
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Sound Interpretation of Leśniewskis Epsilon in Modal Logic KTB
Autorzy:
Inoue, Takao
Powiązania:
https://bibliotekanauki.pl/articles/2033852.pdf
Data publikacji:
2021-11-09
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Le´sniewski’s ontology
propositional ontology
translation
interpretation
modal logic
KTB
soundness
Grzegorczyk’s modal logic
Opis:
In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\), (M2) \(I^M(\neg \phi) = \neg I^M(\phi)\), (M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\), where \(p_a\) and \(p_b\) are propositional variables corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures.
Źródło:
Bulletin of the Section of Logic; 2021, 50, 4; 455-463
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Założeniowe systemy normalnych logik modalnych
Natural Deduction Systems of Normal Modal Logics
Autorzy:
Tkaczyk, Marcin
Powiązania:
https://bibliotekanauki.pl/articles/2013342.pdf
Data publikacji:
2007
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
logika modalna
normalna logika modalna
dedukcja naturalna
system założeniowy
modal logic
normal modal logic
natural deduction
Opis:
Most normal modal logics have been constructed as axiomatic systems rather than natural deduction. However, a lot of them have Gentzen-style or Kalish-Montague-style counterparts. Unfortunately, very few systems have Słupecki-Borkowski-style natural deduction counterparts. To fill in the gap is an aim of the present paper. The system K is developed as a Leśniewski-Borkowski-style natural deduction system in two ways. Equivalence of the systems is proved. A way is described to develop other normal systems beginning with the given system K.
Źródło:
Roczniki Filozoficzne; 2007, 55, 1; 219-228
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
A New Arithmetically Incomplete First-Order Extension of Gl All Theorems of Which Have Cut Free Proofs
Autorzy:
Tourlakis, George
Powiązania:
https://bibliotekanauki.pl/articles/749974.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Modal logic
GL
first-order logic
proof theory
cut elimination
reflection property
disjunction property
quantified modal logic
QGL
arithmetical completeness
Opis:
Reference [12] introduced a novel formula to formula translation tool (“formula-tors”) that enables syntactic metatheoretical investigations of first-order modallogics, bypassing a need to convert them first into Gentzen style logics in order torely on cut elimination and the subformula property. In fact, the formulator tool,as was already demonstrated in loc. cit., is applicable even to the metatheoreticalstudy of logics such as QGL, where cut elimination is (provably, [2]) unavailable. This paper applies the formulator approach to show the independence of the axiom schema ☐A → ☐∀ A of the logics M3and ML3 of [17, 18, 11, 13]. This leads to the conclusion that the two logics obtained by removing this axiom are incomplete, both with respect to their natural Kripke structures and to arithmetical interpretations.  In particular, the so modified ML3 is, similarly to QGL, an arithmetically incomplete first-order extension of GL, but, unlike QGL, all its theorems have cut free proofs. We also establish here, via formulators, a stronger version of the disjunction property for GL and QGL without going through Gentzen versions of these logics (compare with the more complexproofs in [2,8]).
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:
Polyadic algebras over nonclassical logics
Autorzy:
Pigozzi, Don
Salibra, Antonino
Powiązania:
https://bibliotekanauki.pl/articles/1361079.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
lambda calculus
modal logic
intuitionistic logic
many-valued logic
BCK logic
Opis:
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Źródło:
Banach Center Publications; 1993, 28, 1; 51-66
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Zastosowanie systemów pośrednich między S4 A S5 w kontekstach epistemicznych
Application of Systems that are Intermediate between S4 and S5 in Epistemic Contexts
Autorzy:
Lechniak, Marek
Powiązania:
https://bibliotekanauki.pl/articles/2012906.pdf
Data publikacji:
2010
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
logika modalna
systemy logiki modalnej
wiedza
przekonanie
pojęcia epistemiczne
modal logic
systems of modal logic
knowledge
belief
epistemic concepts
Opis:
The article presents systems of modal logics that are stronger than the S4 and weaker than the S5 systems. After a syntactic and semantic presentation of the systems, they are presented as applied to expressing the property of time. Then, after a discussion of some of Hintikka’s arguments concerning “the only” logic proper for the concept of knowledge and belief, against the background of a discussion of various concepts of knowledge and convictions, the application of the S4.2, S4.3, S4F systems as well as of the S4.4 system for expressing properties of epistemic concepts is shown.
Źródło:
Roczniki Filozoficzne; 2010, 58, 2; 41-60
0035-7685
Pojawia się w:
Roczniki Filozoficzne
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:
New Modification of the Subformula Property for a Modal Logic
Autorzy:
Takano, Mitio
Powiązania:
https://bibliotekanauki.pl/articles/1023185.pdf
Data publikacji:
2020-11-04
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
subformula property
modal logic
sequent calculus
scope of □
Opis:
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 natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability for the logic follows from this.
Źródło:
Bulletin of the Section of Logic; 2020, 49, 3; 255-268
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Modified Subformula Property for the Modal Logic S4.2
Autorzy:
Takano, Mitio
Powiązania:
https://bibliotekanauki.pl/articles/749870.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
modal logic S4.2
sequent calculus
subformula property
Opis:
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 shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of □ in some formula of S. These are just the K5-subformulas of some formula in S which were introduced by us to show the modied subformula property for the modal logics K5 and K5D (Bull Sect Logic 30(2): 115–122, 2001). Some corollaries including the interpolation property for S4.2 follow from this. By slightly modifying the proof, the finite model property also follows.
Źródło:
Bulletin of the Section of Logic; 2019, 48, 1
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus
Autorzy:
Indrzejczak, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/749928.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Modal logic S5
decidability
normal forms
sequent calculus
Opis:
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 some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi (SC) for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form.
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
Wyświetlanie 1-15 z 43

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