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Wyszukujesz frazę "modal logic" wg kryterium: Temat


Tytuł:
„Normy wirtualne” a obowiązki realne. O instrumentalnym wynikaniu norm i jego konsekwencjach dla prakseologicznej prawidłowości zmian w prawie
„Virtual Norms” but Real Obligations. On Instrumental Inference of Legal Norms and its Consequences for Praxeological Correctness of Changes in Law
Autorzy:
Zajęcki, Maurycy
Powiązania:
https://bibliotekanauki.pl/articles/2082859.pdf
Data publikacji:
2021
Wydawca:
Akademia Leona Koźmińskiego w Warszawie
Tematy:
teoria prawa
normy prawne
legislacja
inferencja modalna
logika norm
vacatio legis
Trybunał Konstytucyjny
theory of law
legal norms
legislation
modal inference
logic of norms
Constitutional Tribunal
Opis:
Artykuł podejmuje problematykę inferencji modalnej: jeśli adresaci normy mają nakazane coś czynić, zobowiązani są także zrealizować stany rzeczy, które są warunkiem niezbędnym dla zrealizowania zasadniczego obowiązku; analogicznie, są oni zobowiązani do powstrzymania się od zrealizowania stanów rzeczy, które są warunkiem wystarczającym, by zasadniczy obowiązek nie mógł być zrealizowany. Te typy inferencji są nazywane w polskiej teorii prawa „wynikaniem instrumentalnym”. Twierdzi się w artykule, że czasami normy instrumentalne muszą być zrealizowane (inaczej: muszą być podjęte „czynności wstępne”) zanim zrealizowany zostanie obowiązek zasadniczy. Prawodawca pomaga adresatom poprzez oznaczenie odpowiedniej vacatio legis. To może prowadzić do dalszych paradoksalnych konsekwencji – do kreacji „norm wirtualnych” – norm, które nigdy nie wchodzą w życie, ale ich adresaci są zobowiązani do podjęcia czynności przygotowawczych. Artykuł stara się opisać teoretycznie to zjawisko. W konkluzji postawiona zostaje jedna hipoteza dogmatyczna: czynności przygotowawcze, które nałożyły na adresatów realny ciężar czynności przygotowawczych, mogą rodzić po stronie organów władzy publicznej obowiązek kompensacyjny (art. 4171 § 1 k.c.), jeśli obowiązek zasadniczy okaże się być „wirtualny”. W Polsce organem mogącym stwierdzić zajście opisanej przesłanki jest Trybunał Konstytucyjny.
The article deals with the problem of modal inference: if some addressees are obliged to do something, they are also obliged to realize states of affairs which constitute a necessary condition for the main obligation. Likewise, they are obliged to refrain from realizing states of affairs which constitute a sufficient condition for the action contradicting the main obligation. This type of inference is called in Polish legal theory “instrumental inference”. It is argued in the article that sometimes instrumental norms in law must be fulfilled (“preparatory actions” must be undertaken) before the main obligation is fulfilled. Lawgiver helps addressees of norms by applying vacatio legis. It can lead to new paradoxical consequences – to the creation of “virtual norms” – norms which never come into force, but addressees are obliged to undertake preparatory actions. The article presents theoretical description of this phenomenon. In conclusion one dogmatic claim is proposed: there is a potential way (art. 4171 § 1 k.c.) of getting from public officials compensation for preparatory actions which caused burden for addressees, when the main obligation turned out to be “virtual”. In Poland this procedure should be based on the rulings of the Constitutional Tribunal.
Źródło:
Krytyka Prawa. Niezależne Studia nad Prawem; 2021, 13, 2; 227-247
2080-1084
2450-7938
Pojawia się w:
Krytyka Prawa. Niezależne Studia nad Prawem
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A certain approach to Kripke semantics for normal modal logics
Autorzy:
Bryll, G.
Sochacki, R.
Powiązania:
https://bibliotekanauki.pl/articles/121860.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
logika modalna
semantyka Kripke
logika czasowa
logika matematyczna
modal logic
Kripke’s semantics
mathematical logic
Opis:
In this paper the authors propose a method of verifying formulae in normal modal logics. In order to show that a formula α is a thesis of a normal modal logic, a set of decomposition rules for any formula is given. These decomposition rules are based on the symbols of assertion and rejection of formulae.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 13-20
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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:
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:
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:
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 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:
All splitting logics in the lattice NEXT(KTB:30A)
Autorzy:
Kostrzycka, Z.
Powiązania:
https://bibliotekanauki.pl/articles/121995.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
logika modalna
ramka Kripkego
klastry rozłączne
modal logic
Kripke’s frome
disjoint clusters
Opis:
We examine a special modal logic which is a normal extension of the Brouwer modal logic. It is determined by linearly ordered chains of clusters and the relation between clusters is reflexive and symmetric. The appropriate axiomatization of this logic is proposed in the papers [11] and [12]. There is also proved that all normal extensions of the investigated logic are Kripke complete and have f.m.p. Unfortunately, the cardinality of this family is continuum [13]. One may imagine that the structure of the lattice of these extensions is immensely complex. Then we use the technics of splitting to characterize this lattice and to describe some quite simple fragments. We characterize all the logics that split the lattice.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2016, 21; 31-61
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An Arithmetically Complete Predicate Modal Logic
Autorzy:
Hao, Yunge
Tourlakis, George
Powiązania:
https://bibliotekanauki.pl/articles/2033850.pdf
Data publikacji:
2021-08-23
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
Predicate modal logic
arithmetic completeness
logic GL
Solovay's theorem
equational proofs
Opis:
This paper investigates a first-order extension of GL called \(\textup{ML}^3\). We outline briefly the history that led to \(\textup{ML}^3\), its key properties and some of its toolbox: the \emph{conservation theorem}, its cut-free Gentzenisation, the ``formulators'' tool. Its semantic completeness (with respect to finite reverse well-founded Kripke models) is fully stated in the current paper and the proof is retold here. Applying the Solovay technique to those models the present paper establishes its main result, namely, that \(\textup{ML}^3\) is arithmetically complete. As expanded below, \(\textup{ML}^3\) is a first-order modal logic that along with its built-in ability to simulate general classical first-order provability―"\(\Box\)" simulating the the informal classical "\(\vdash\)"―is also arithmetically complete in the Solovay sense.
Źródło:
Bulletin of the Section of Logic; 2021, 50, 4; 513-541
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bóg, modalność, esencjalizm. Pewna wersja szkotystycznego dowodu tezy o istnieniu Boga
God, Modality and Essentialism. A Version of the Scotist Proof for God’s Existence
Autorzy:
Tkaczyk, Marcin
Powiązania:
https://bibliotekanauki.pl/articles/2013049.pdf
Data publikacji:
2009
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
Duns Szkot
dowód na istnienie Boga
logika modalna
esencjalizm
Duns Scotus
proof for God’s existence
modal logic
essentialism
Opis:
A proof for God’s existence, inspired by Duns Scotus’s Tractatus de primo principio, is analyzed. The conclusion is based on three premises arranged in the matrix of a specific modal logic. The premises are: 1. it is possible for the world to be created by God; 2. if the world is created by God, then God exists; 3. if God exists, then God exists necessarily. In comparison to the original Scotus’s work the concept of essential order has been removed and replaced with a concept of creation. Modal expressions of the proof have been analyzed with an application of essentialism of Aristotle and Ibn Sina – the version of essentialism accepted by Scotus. Scotus’s underlying modal logic has been reconstructed and discussed in two versions: 1. as a modal logic with one pair of natural modalities; 2. as a multimodal logic with two pairs of modalities – natural and logical. The concept of natural modality is based on the essentialism discussed, the concept of logical modality is based on Scotus’s idea of non repugnantia terminorum.
Źródło:
Roczniki Filozoficzne; 2009, 57, 1; 231-256
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödels Ontological Argument
Autorzy:
Benzmüller, Christoph
Fuenmayor, David
Powiązania:
https://bibliotekanauki.pl/articles/750054.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
computational metaphysics
ontological argument
higher-order modal logic
higher-order logic
automated reasoning
modal ultrafilters
Opis:
Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the utilization of suitably adapted notions of (modal) ultrafilters, and a careful distinction between extensions and intensions of positive properties.
Źródło:
Bulletin of the Section of Logic; 2020, 49, 2
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cut Elimination for Extended Sequent Calculi
Autorzy:
Martini, Simone
Masini, Andrea
Zorzi, Margherita
Powiązania:
https://bibliotekanauki.pl/articles/43182562.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
proof theory
sequent calculus
cut elimination
modal logic
2-sequents
Opis:
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 \(\mathsf{S4}\) spectrum. We design the systems uniformly since they all share the same set of rules. Different logics are obtained by “tuning” a single parameter, namely a constraint on the applicability of the cut rule and on the (left and right, respectively) rules for \(\Box\) and \(\Diamond\). Starting points for this research are 2-sequents and indexed-based calculi (sequents and tableaux). By extending and modifying existing proposals, we show how to achieve a syntactical proof of the cut-elimination theorem that is as close as possible to the one for first-order classical logic. In doing this, we implicitly show how small is the proof-theoretical distance between classical logic and the systems under consideration.
Źródło:
Bulletin of the Section of Logic; 2023, 52, 4; 459-495
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:
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:
Identity, equality, nameability and completeness. Part II
Autorzy:
Manzano, María
Moreno, Manuel Crescencio
Powiązania:
https://bibliotekanauki.pl/articles/749980.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
identity
equality
completeness
nameability
first-order modal logic
hybrid logic
hybrid type theory
equational hybrid propositional type theory
Opis:
This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity is a notion used to define other logical concepts. In our previous paper, [16], we investigated whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic with standard semantics a reliable definition of identity is possible. In the present study we have moved to modal logic and realized that here we can distinguish in the formal language between two different equality symbols, the first one shall be interpreted as extensional genuine identity and only applies for objects, the second one applies for non rigid terms and has the characteristic of synonymy. We have also analyzed the hybrid modal logic where we can introduce rigid terms by definition and can express that two worlds are identical by using the nominals and the @ operator. We finish our paper in the kingdom of identity where the only primitives are lambda and equality. Here we show how other logical concepts can be defined in terms of the identity relation. We have found at the end of our walk a possible point of convergence in the logic Equational Hybrid Propositional Type Theory (EHPTT), [14] and [15].
Źródło:
Bulletin of the Section of Logic; 2018, 47, 3
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł

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