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    Wyświetlanie 1-14 z 14
    Tytuł:
    Valuation graphs for propositional logic
    Autorzy:
    Stępień, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/121964.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    valuation graphs
    propositional logic
    wykresy wyceny
    rachunek zdań
    Opis:
    In this paper we present the proof system, called the valuation graphs system, which is a new version of two proof procedures: Davis-Putnam and Stålmarck. The novelty is that in the rules we note which propositional variable occurring in some propositional formula does not determine the logical value of that formula. Due to Stålmarck, we define a notion of proof width, corresponding to the width of structure of valuation graph which is a number of applications of dilemma rule. The dilemma rule considers two cases, so the time of proof grows up exponentially.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2010, 15; 139-148
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    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:
    The Method of Socratic Proofs Meets Correspondence Analysis
    Autorzy:
    Leszczyńska-Jasion, Dorota
    Petrukhin, Yaroslav
    Shangin, Vasilyi
    Powiązania:
    https://bibliotekanauki.pl/articles/749950.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Socratic proofs
    correspondence analysis
    invertible rule
    inferential erotetic logic
    classical propositional logic
    sequent calculus
    Opis:
    The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.
    Źródło:
    Bulletin of the Section of Logic; 2019, 48, 2; 99-116
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Four-valued expansions of Dunn-Belnaps logic (I): Basic characterizations
    Autorzy:
    Pynko, Alexej P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1023300.pdf
    Data publikacji:
    2020-12-30
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    propositional logic
    logical matrix
    Dunn-Belnap's logic
    expansion
    [bounded] distributive/De Morgan lattice
    equality determinant
    Opis:
    Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 4 of a De Morgan non-Boolean four-valued diamond, but by no matrix with either less than four values or a single [non-]distinguished value, and has no proper extension satisfying Variable Sharing Property (VSP). We then characterize L4's having a theorem / inconsistent formula, satisfying VSP and being [inferentially] maximal / subclassical / maximally paraconsistent, in particular, algebraically through ℳ4|4's (not) having certain submatrices|subalebras. Likewise, [providing 4 is regular / has no three-element subalgebra] L4 has a proper consistent axiomatic extension if[f] ℳ4 has a proper paraconsistent / two-valued submatrix [in which case the logic of this submatrix is the only proper consistent axiomatic extension of L4 and is relatively axiomatized by the Excluded Middle law axiom]. As a generic tool (applicable, in particular, to both classically-negative and implicative expansions of DB4), we also prove that the lattice of axiomatic extensions of the logic of an implicative matrix ℳ with equality determinant is dual to the distributive lattice of lower cones of the set of all submatrices of ℳ with non-distinguished values.
    Źródło:
    Bulletin of the Section of Logic; 2020, 49, 4; 401-437
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Functional Completeness in CPL via Correspondence Analysis
    Autorzy:
    Leszczyńska-Jasion, Dorota
    Petrukhin, Yaroslav
    Shangin, Vasilyi
    Jukiewicz, Marcin
    Powiązania:
    https://bibliotekanauki.pl/articles/749866.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    correspondence analysis
    invertible rules
    classical propositional logic
    functional completeness
    sequent calculus
    automated deduction
    automated rules generation
    Opis:
    Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional logic. The properties of soundness and completeness of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method. Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness.
    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:
    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:
    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:
    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
    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
    Tytuł:
    Applying propositional calculus of formal logic to formulate research hypotheses in management sciences
    Propozycja wykorzystania rachunku zdań logiki formalnej do tworzenia hipotez badawczych w naukach o zarządzaniu
    Autorzy:
    Pabian, Aleksander
    Powiązania:
    https://bibliotekanauki.pl/articles/2177735.pdf
    Data publikacji:
    2023-02-28
    Wydawca:
    Główny Urząd Statystyczny
    Tematy:
    research hypotheses
    formal logic
    management
    propositional calculus
    hipotezy badawcze
    logika formalna
    zarządzanie
    rachunek zadań
    Opis:
    The article is devoted to the topic of formulating research hypotheses in management sciences. On the basis of the author’s research results, it may be concluded that although the related literature indicates the features of a properly formulated hypothesis, errors still tend to occur in the process of its construction and as a consequence, the answers to the question or questions determining the research problem are not correctly formulated. Examples of such errors include attempts to check statements which are unverifiable in practice, which could be observed even in Master’s theses. The propositional calculus, whose source is in formal logic, may prove a useful tool in creating proper hypotheses. The primary aim of the article is to prove the usefulness of the propositional calculus of formal logic in formulating the main hypothesis and partial hypotheses in research work relating to management sciences. Prior to adopting a hypothesis for further proceedings, it should be decomposed into prime factors, followed by an analysis of the propositions. Adopting such a calculus when formulating each hypothesis should result in their comprehensible and logical form, compliant with linguistic rules.
    Tematem artykułu jest formułowanie hipotez badawczych w naukach o zarządzaniu. Na podstawie wyników badania przeprowadzonego przez autora można stwierdzić, że choć w literaturze przedmiotu wskazywane są cechy prawidłowo sformułowanej hipotezy, to podczas tworzenia hipotez badawczych często dochodzi do błędów, a w konsekwencji odpowiedzi na pytanie (pytania) wyrażające problem badawczy są skonstruowane niepoprawnie. Przykłady takich błędów, m.in. próby sprawdzenia w praktyce stwierdzeń nieweryfikowalnych, można znaleźć nawet w pracach magisterskich. W tworzeniu poprawnych hipotez pomocny może być rachunek zdań mający źródło w logice formalnej. Celem artykułu jest udowodnienie przydatności rachunku zdań logiki formalnej w formułowaniu hipotezy głównej i hipotez cząstkowych w pracach badawczych z zakresu nauk o zarządzaniu. Przed przyjęciem hipotezy należy rozłożyć ją na czynniki pierwsze i przeprowadzić analizę zdań. Zastosowanie takiej procedury powinno doprowadzić do nadania każdej z hipotez zrozumiałej i logicznej postaci oraz zapewnić ich zgodność z regułami językowymi.
    Źródło:
    Wiadomości Statystyczne. The Polish Statistician; 2023, 68, 2; 39-55
    0043-518X
    Pojawia się w:
    Wiadomości Statystyczne. The Polish Statistician
    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:
    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:
    Logicy i logika a poznanie przyrody
    Logicians and Logic on Study of Nature
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/2013931.pdf
    Data publikacji:
    2005
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika
    funktor prawdziwościowy
    funktor nieprawdziwościowy
    dwuwartościowy rachunek zdań
    wielowartościowy rachunek zdań
    logic
    truth-functional operator
    not truth-functional operator
    two valued propositional calculus
    many-valued propositional calculus
    Opis:
    Starting from the 1930s logicians tackled problems connected with applicability of logic in natural sciences and in many cases they tried to practically apply logic in these sciences. In the article entitled ‘Logicians and logic on study of nature’ it is stressed that the broadly understood formal logic supplies natural sciences, and especially physics, with a paradigm for a method of ordering theses. It is also shown what application of logic laws to natural sciences consists in, and theses are formulated concerning what the laws of classical propositional calculus state. A lot of attention is devoted to the language of modern and contemporary physics. Modern and contemporary physics uses two languages, i.e. the mathematical language and the so-called notional language. The logic of the former language is classical logical calculus. In connection with the notional language logicians construed a lot of systems of non-classical logics in which laws are given that govern the correct use of non-extensional operators connected with such terms occurring in natural sciences as “time”, “cause”, “change” etc. The language of well construed systems of non-classical logics may serve saving, storing and precise communicating the results obtained on the ground of natural sciences.
    Źródło:
    Roczniki Filozoficzne; 2005, 53, 1; 129-142
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    O NIEKTÓRYCH PRAWACH LOGIKI I ZASADACH OGÓLNEJ TEORII BYTU
    Autorzy:
    Kiczuk, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/488533.pdf
    Data publikacji:
    2012
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    logika współczesna
    funktor prawdziwościowy
    klasyczny rachunek zdań
    zasada racji dostatecznej
    modern logic
    truth-functional operator
    classical propositional calculus
    principle of sufficient reason
    Opis:
    Some principles of general theory of being have their equivalents in laws of classical logic. For a long time this was not distinctly noticed, as logic was treated rather as technology of discussion, and not as a system of propositions stated in the objective language and concerning connections between facts. It may be generally said that some primary principles of being and some laws of logic state the same most fundamental connections between facts, between states of things. There are also principles of philosophy that do not have such equivalents in laws of logic. These include the principle of sufficient reason. The concept of intuitive truth of propositions that reappeared in modern logic first of all in connection with K. Gödel’s theorem of 1931 formed an intellectual climate that made it possible for classical logicians to accept also those principles of general theory of being that do not have equivalents in laws of standard logic. It may be said that these philosophical principles may be included in the outward basis of modern logic.
    Źródło:
    Roczniki Filozoficzne; 2012, 60, 2; 171-179
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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