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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:
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:
Teoria kategorii i niektóre jej logiczne aspekty
Category theory and some of its logical aspects
Autorzy:
Stopa, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/690940.pdf
Data publikacji:
2018
Wydawca:
Copernicus Center Press
Tematy:
category theory
topos theory
categorical logic
propositional logic
intuitionistic logic
non-classical logic
Opis:
This article is intended for philosophers and logicians as a short partial introduction to category theory (CT) and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2018, 64; 7-58
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
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:
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:
On the validity of the definition of a complement-classifier
Autorzy:
Stopa, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/1047622.pdf
Data publikacji:
2020-12-29
Wydawca:
Copernicus Center Press
Tematy:
category theory
topos theory
categorical logic
Heyting algebras
co-Heyting algebras
intuitionistic logic
dual to intuitionistic logic
complement-classifier
Opis:
It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes (co-toposes), which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier (and thus of a co-topos as well) is, at least in general and within the conceptual framework of category theory, not appropriately defined. For this purpose, I first analyze the standard notion of a subobject classifier, show its connection with the representability of the functor Sub via the Yoneda lemma, recall some other properties of the internal structure of a topos and, based on these, I critically comment on the notion of a complement-classifier (and thus of a co-topos as well).
Źródło:
Zagadnienia Filozoficzne w Nauce; 2020, 69; 111-128
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the concept of truth in an intended model of the logic of beliefs
O pojęciu prawdy w modelu zamierzonym logiki przekonań
Autorzy:
Wesserling, Janusz
Nieznański, Edward
Powiązania:
https://bibliotekanauki.pl/articles/431129.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Kardynała Stefana Wyszyńskiego w Warszawie
Tematy:
logic of beliefs
intuitionistic logic
semantics of intended models
concept of truth
logika przekonań
logika intuicjonistyczna
semantyka modeli zamierzonych
pojęcie prawdy
Opis:
First of all the article looks at the building of an a posteriori logic of beliefs i.e. observation developed on the principle of how, people usually think, what kind of judgments they make about reality and what actually is described by the truth of the judgments under the influences of beliefs. In this situation, we have to depart from the customary practice of a priori semantics of possible worlds in favour of semantics for models intended. Secondly, we find that in practice, human judgments indirectly accept a logic of thinking generally, which leads us - thirdly - to define this logical system as an extension of intuitionistic logic. Fourthly, and finally, our empirically generated logic of beliefs, proves to be logic of hypotheses and suppositions, because judgments made on the basis of intuitionistic logic are not assertive judgments.
W artykule chodzi – po pierwsze – o zbudowanie aposteriorycznej logiki przekonań, czyli wypracowanej na zasadzie obserwacji, jak ludzie zwykle myślą, jakiego rodzaju sądy wydają o rzeczywistości i jakiej rzeczywistości dotyczy prawda sądów, którymi rządzą przekonania. W tej sytuacji musimy odstąpić od zwyczaju uprawiania apriorycznej semantyki światów możliwych na rzecz semantyki modeli zamierzonych. Po wtóre, odnajdujemy, że w praktyce ludzkiego wydawania sądów, pośrednią rolę pełni pewnego rodzaju logika myślenia w ogóle, której metajęzykowy rozbiór skłania nas – po trzecie – do określenia jej jako systemu nadbudowanego nad logiką intuicjonistyczną. A po czwarte, nasza logika przekonań, empirycznie generowana, okazała się być logiką przekonań hipotetycznych i supozycyjnych, ponieważ sądy wydawane na gruncie logiki intuicjonistycznej nie są sądami asertywnymi.
Źródło:
Studia Philosophiae Christianae; 2013, 49, 1; 135-149
0585-5470
Pojawia się w:
Studia Philosophiae Christianae
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:
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:
Geneza intuicjonistycznego rachunku zdań i Twierdzenie Gliwienki
The Origin of Intuitionistic Propositional Calculus and Glivenko’s Theorem
Autorzy:
Urbańczyk, Piotr
Powiązania:
https://bibliotekanauki.pl/articles/691110.pdf
Data publikacji:
2014
Wydawca:
Copernicus Center Press
Tematy:
Glivenko’s theorem
intuitionistic logic
intuitionistic propositional calculus
history of logic
history of mathematics
Opis:
Among the non-classical logics, the intuitionistic one stands out in many ways. First of all, because of its properties, it is grateful subject of formal analysis. Moreover, there is small, but very significant group of mathematicians and philosophers who claim that intuitionistic logic captures the reasoning utilized in mathematics better than classical one. This article reveals the origins of intuitionistic propositional calculus – it was an outcome of formalization of certain ideas about foundations of mathematics. A large part of the article is devoted to Glivenko’s Theorem – somewhat forgotten, but extremely interesting formal result regarding the relationship between the two logical calculi: classical and intuitionistic propositional logic.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2014, 56; 33-56
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
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:
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:
CZYM JEST PLURALIZM LOGICZNY? (STANOWISKO J.C. BEALLA I GREGA RESTALLA)
WHAT IS LOGICAL PLURALISM? (J.C. BEALL’S AND GREG RESTALL’S STANDPOINT)
Autorzy:
Czernecka-Rej, Bożena
Powiązania:
https://bibliotekanauki.pl/articles/488487.pdf
Data publikacji:
2013
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
pluralizm logiczny
wynikanie logiczne
poprawny system logiczny
logika klasyczna
logika intuicjonistyczna
logika relewantna
logical pluralism
logical consequence
correct logical system
classical logic
intuitionistic logic
relevant logic
Opis:
C. Beall and Greg Restall are advocates of a comprehensive pluralist approach to logic, which they call Logical Pluralism (LP). According to LP, there is not one correct logic, but many equally acceptable logical systems. The authors share Tarski’s conviction and follow the mainstream in thinking about logic as the discipline that investigates the notion of logical consequence. LP is the pluralism about logical consequence – a pluralist maintains that there is more than one relation of logical consequence. According to LP, classical, intuitionistic and relevant logics are not rivals, but they all are equally correct, they all count as genuine logics. The purpose of this paper is to present some remarks concerning J.C. Beall’s and Greg Restall’s exposition of LP. At the beginning, the definition of the relation of logical consequence, which is central to their proposal, is shown. According to Beall and Restall, argument is valid if, and only if, in every case when the premisses are true, then the conclusion is, too. They argue that by considering different types of cases the logical pluralist obtains different logics. The paper — apart from presenting LP — also gives a critical discussion of this approach. It seems, that the thesis of LP is far from being clear. It is even unclear what exactly LP is and where is stops. It is unclear what “equally good”, “equally correct”, “equally true” mean. It is not clear, how to explain, in scope of logic, that the system of logic, is a model of real logical connections.
Źródło:
Roczniki Filozoficzne; 2013, 61, 1; 5-22
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Basic properties of a new class of parametric intuitionistic fuzzy implications
Autorzy:
Dworniczak, P.
Powiązania:
https://bibliotekanauki.pl/articles/206173.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
parametric fuzzy implication
intuitionistic fuzzy logic
Opis:
In this paper a new class of intuitionistic fuzzy implications is introduced. Fulfillment of some axioms and properties together with Modus Ponens and Modus Tollens inference rules is investigated. Negation induced by implication is presented.
Źródło:
Control and Cybernetics; 2011, 40, 3; 793-804
0324-8569
Pojawia się w:
Control and Cybernetics
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
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