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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
Wyświetlanie 1-10 z 14

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