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    Wyświetlanie 1-8 z 8
    Tytuł:
    Praktyczny aspekt logiki (stanowisko Kazimierza Ajdukiewicza)
    The Practical Aspect of Logic from the Standpoint of Kazimierz Ajdukiewicz
    Autorzy:
    Czernecka-Rej, Bożena
    Powiązania:
    https://bibliotekanauki.pl/articles/468752.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Instytut Filozofii i Socjologii PAN
    Tematy:
    Ajdukiewicz Kazimierz
    first-order logic
    logical culture
    practical science
    Opis:
    The aim of this article is to present and discuss the Ajdukiewicz’s concept of the practical aspect of logic. To begin, I describe his concept of the practical importance of science and especially his concept of logic – i.e., the definition and range of logic. The idea of “logical culture” is fundamental to his conceptualization. I also present Ajdukiewicz’s idea that making the course of logic more practical should be required. At the end of the article I discuss the importance of Ajdukiewicz’s view.
    Źródło:
    Prakseologia; 2012, 152; 223-235
    0079-4872
    Pojawia się w:
    Prakseologia
    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:
    Identity, Equality, Nameability and Completeness
    Autorzy:
    Manzano, María
    Moreno, Manuel Crescencio
    Powiązania:
    https://bibliotekanauki.pl/articles/750030.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    first-order logic
    type theory
    identity
    equality
    indiscernibility
    comprehension
    completeness
    translations
    nameability
    Opis:
    This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first case, one investigates what kind of logic is required. In the second case, one is interested in the definition of the other logical concepts (connectives and quantifiers) in terms of the identity relation, using also abstraction. The present paper investigates whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic a reliable definition of identity is possible. However, the definition needs the standard semantics and we know that with this semantics completeness is lost. We have also studied the relationship of equality with comprehension and extensionality and pointed out the relevant role played by these two axioms in Henkin’s completeness method. We finish our paper with a section devoted to general semantics, where the role played by the nameable hierarchy of types is the key in Henkin’s completeness method.
    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
    Tytuł:
    Universality of Logic
    Autorzy:
    Woleński, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/749938.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    universality
    logica docents
    logica utens
    first-order logic
    consequence operation
    model
    syntax
    semantics
    expressive power
    Opis:
    This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity (truth in all models). All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic. The categorical approach to logic is presented as associated with the last understanding of universality. The author concludes that two senses of universality should be sharply discriminated and defends the first-order thesis.
    Źródło:
    Bulletin of the Section of Logic; 2017, 46, 1/2
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modeling of distributed objects computing pattern combinations using a formal specification language
    Autorzy:
    Taibi, T.
    Ngo, D. C. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/908185.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    informatyka
    Balanced Pattern Specification Language (BPSL)
    First-Order Logic (FOL)
    Temporal Logic of Actions (TLA)
    substitution
    addition
    elimination
    Opis:
    Design patterns help us to respond to the challenges faced while developing Distributed Object Computing (DOC) applications by shifting developers' focus to high-level design concerns, rather than platform specific details. However, due to the inherent ambiguity of the existing textual and graphical descriptions of the design patterns, users are faced with difficulties in understanding when and how to use them. Since design patterns are seldom used in isolation but are usually combined to solve complex problems, the above-mentioned difficulties have even worsened. The formal specification of design patterns and their combination is not meant to replace the existing means of describing patterns, but to complement them in order to achieve accuracy and to allow rigorous reasoning about them. The main problem of the existing formal specification languages for design patterns is the lack of completeness. This is mainly because they tend to focus on specifying either the structural or behavioral aspects of design patterns but not both of them. Moreover, none of them even ventured in specifying DOC patterns and pattern combinations. We propose a simple yet Balanced Pattern Specification Language (BPSL) aimed to achieve equilibrium by specifying both the aspects of design patterns. The language combines two subsets of logic: one from the First-Order Logic (FOL) and the other from the Temporal Logic of Actions (TLA).
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 239-253
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    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:
    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:
    On Four Types of Argumentation For Classical Logic
    O czterech typach argumentacji na rzecz logiki klasycznej
    Autorzy:
    Czernecka-Rej, Bożena
    Powiązania:
    https://bibliotekanauki.pl/articles/1791005.pdf
    Data publikacji:
    2021-01-04
    Wydawca:
    Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
    Tematy:
    teza o logice I rzędu
    maksyma minimalnego okaleczania
    uniwersalność logiki
    logika rzeczy
    metalogika
    W.v.O. Quine
    J. Woleński
    S. Kiczuk
    first-order thesis
    maxim of minimum mutilation
    universality of logic
    logic of things
    metalogic
    Opis:
    My goal of this article is to analyze the argumentation lines for the correctness of standard logic. I also formulate a few critical and comparative remarks. I focus on four the most coherent and complete argumentations which try to justify the distinguished position of classical logic. There are the following argumentations: Willard van O. Quine’s pragmatic-methodological argumentation, Jan Woleński’s philosophical-metalogical argumentation, Stanisław Kiczuk’s ontological-semantic argumentation, argumentation based on metalogic. In my opinion, the thesis concerning the correctness of classical logic is rationally justified by these argumentations. The problem remains whether the analyzed standard logic is the only proper logic.
    Moim celem w tym artykule jest analiza argumentacji pod kątem poprawności standardowej logiki. Formułuję też kilka uwag krytycznych i porównawczych. Skupiam się na czterech najbardziej spójnych i kompletnych argumentach, które próbują uzasadnić wyróżnione stanowisko logiki klasycznej. Istnieją następujące argumenty: argumentacja pragmatyczno-metodologiczna Willarda van O. Quine’a, argumentacja filozoficzno-metalogiczna Jana Woleńskiego, argumentacja ontologiczno-semantyczna Stanisława Kiczuka, argumentacja metalogiczna. Moim zdaniem teza o poprawności logiki klasycznej jest racjonalnie uzasadniona tymi argumentacjami. Pozostaje problem, czy analizowana logika standardowa jest jedyną właściwą logiką.
    Źródło:
    Roczniki Filozoficzne; 2020, 68, 4; 271-289
    0035-7685
    Pojawia się w:
    Roczniki Filozoficzne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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