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    Wyświetlanie 1-8 z 8
    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:
    Uwagi o systemie logiki formalnej skonstruowanym dla logików nieformalnych
    Remarks on the System of Formal Logic Construed for Informal Logicians
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/2012940.pdf
    Data publikacji:
    2010
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    funktor prawdziwościowy
    logika nieformalna
    logika nieklasyczna
    klasyczny rachunek zdań
    truth-functional operator
    informal logic
    non-classical logic
    classical propositional calculus
    Opis:
    D. Sherry’s main theses included in his essay entitled “Formal Logic for Informal Logicians” are presented in the article. In a discussion with his theses it is shown that he prefers this kind of logic that has a lot of elements that are the same as in Aristotle’s logic understood as the art of thinking and the technique of discussion taken from Topics, and not the logic that was started in his Prior Analytics. It is also shown that not only patterns of inferring, but also the theses of logic, as well as theses to which no patterns correspond, that are guarantee reliability of inference patterns, may be intuitively obvious. In the article also attention is drawn to the fact that the PL- system of logic presented by Sherry was characterized by him by means of a rather poor logical terminology. In the American author’s argument there are no clear distinctions between the thesis of logic, the logical inference pattern and the rule of the procedure of proving. However, it can be established that the PL- system is constituted by argumentation patterns that are reliable owing to such theses of propositional logic as modus potens, modus tollens, disjunctive syllogism, conjunctive syllogism, complex destructive dilemma, and the two rules concerning creating proofs, i.e. the rule of conditional proof and the rule of reduction to the absurd. In the PL- system there are fewer theses than in the classical propositional calculus, but this has nothing in common with the so-called multivalent logics to which some theses of classical logic supposedly do not apply. Everything suggests that some systems of non-classical logic systems may be built on the PL- system; namely, the ones in which theses are given that govern the correct use of non-extensional operators connected with key terms appearing in many sciences, like e.g. “time”, “change”, “causality”. Sherry’s essay reveals that he is a supporter of the thesis that knowledge of formal logic is necessary for using informal logic efficiently, which is necessary for teaching logic properly.
    Źródło:
    Roczniki Filozoficzne; 2010, 58, 1; 95-108
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    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:
    Logika formalna czy logiki formalne?
    Formal Logic or Formal Logics?
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/2013349.pdf
    Data publikacji:
    2007
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika
    funktor prawdziwościowy
    logika standardowa
    logika nieklasyczna
    wielowartościowy rachunek zdań
    logika klasyczna
    logic
    truth-functional operator
    standard logic
    non-classical logic
    many-valued propositional calculus
    classical logic
    Opis:
    Apart from putting the theses contained in E. Agazzi’s work Why Is It Logical to Admit Several Logics? in an order and making them more distinct, an attempt is made to draw conclusions from the explicit wordings used by that author. Some theses presented in the text are shown against the views of other authors who discussed analogous problems. In this way, as it seems, modification, completing and elaborating has been possible of wordings that approve of the thesis about the existence of many logics that are contained in the analyzed text. Among others, the article emphasizes that Agazzi’s pronouncements about relations existing between standard logic and intuitionist logic cannot be accepted. Also, several remarks are made about the so-called many-valued logics. Agazzi’s theses that well constructed non-classical logics representing proper contents are necessary for representatives of various branches of knowledge is acceptable.
    Źródło:
    Roczniki Filozoficzne; 2007, 55, 1; 129-157
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    „O pewnym kryterium wyboru poprawnej logiki. Na marginesie uwag Ananda J. Vaidyi
    The Criterion of the Choice of a Correct Logic. On Anand J. Vaidya’s Remarks
    Autorzy:
    Czernecka-Rej, Bożena
    Powiązania:
    https://bibliotekanauki.pl/articles/2013033.pdf
    Data publikacji:
    2009
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    poprawny system logiczny
    stała logiczna
    prawo logiki
    logika klasyczna i nieklasyczna
    metafizyczny determinizm
    correct logical system
    logical constant
    law of logic
    classical and non-classical logic
    metaphysical determinism
    Opis:
    The purpose of this paper is to show the criterion of the choice of a correct logic. According to Vaidya such the criterion may be formulated only on the foundation of a philosophy of logic. The main elements of the laws of logic are logical constants. In fact logic is not the theory of variables, but the theory of logical constants. So, the goal of a correct logical system is to analyse in a proper way what logical constants are.
    Źródło:
    Roczniki Filozoficzne; 2009, 57, 2; 41-60
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Opis szeregujący a logiki wielowartościowe. J. N. Martina próba interpretacji systemu Łukasiewicza
    Ordering description and many-valued logics. J. N. Martin’s attempt at interpretation of Lukasiewicz’s system
    Autorzy:
    Lechniak, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/2016146.pdf
    Data publikacji:
    2001
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika nieklasyczna. logika wielowartościowa
    negacje
    historia filozofii
    neoplatonizm
    podział logiczny
    klasyfikacja
    szeregowanie
    non-classical logic
    many-valued logic
    negation(s)
    history of philosophy
    neoplatonism
    logical division
    classification
    ordering
    Opis:
    The article presents two attempts at applying J. Lukas iewicz's three-valued logic to analysis of the so-called gradable properties: T. Czeżowski's so-called ordering logics and J. Martin's attempt to connect Lukas iewicz's logic and the neo-Platonian hierarchy of entities. Unfortunately, those attempts were not successful. It can be noticed that in his approach Czeżowski mixed up gradability of truth with gradability of other properties. Martin found that Lukasiewicz's enriching of the division between truth and falsity with a third value suggests some neo-Platonian ontology in which truth - interchangeable with entity - is subject to gradation. However, he does not give an intuitively convincing way of reducing Lukas iewicz's threevalued logic to the corresponding Boole's algebra of compound properties (hence, to a structure belonging to the classical logic).
    Źródło:
    Roczniki Filozoficzne; 2001, 49, 1; 167-183
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E
    Autorzy:
    Typańska-Czajka, Lidia
    Powiązania:
    https://bibliotekanauki.pl/articles/749872.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    relevant logic
    non-classical logics
    lattice
    universal algebra
    Opis:
    The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].
    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:
    Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2
    Autorzy:
    Mruczek-Nasieniewska, Krystyna
    Nasieniewski, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/750018.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    non-classical negation
    modalized negation
    impossibility
    correspondence
    regular modal logics
    the smallest regular deontic logic D2
    Opis:
    In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9]). In (Došen; [2]) a logic N has been investigated in the language with negation; implication; conjunction and disjunction by axioms of positive intuitionistic logic; the right-to-left part of the second de Morgan law; and the rules of modus ponens and contraposition. From the semantical point of view the negation used by Došen is the modal operator of impossibility. It is known this operator is a characteristic of the modal interpretation of intuitionistic negation (see [3; p. 300]). In the present paper we consider an extension of N denoted by N+. We will prove that every extension of N+ that is closed under the same rules as N+; corresponds to a regular logic being an extension of the regular deontic logic D21 (see [4] and [13]). The proved correspondence allows to obtain from soundnesscompleteness result for any given regular logic containing D2, similar adequacy theorem for the respective extension of the logic N+.
    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
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