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1
Content available Kłamię
Gawron Piotr
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
2023
|
Nr 5
251-255
PL
Podajemy przykłady paradoksów z różnych epok, poczynając od starożytnego paradoksu kłamcy do paradoksów Russella.
2
Content available Giuseppe Peano in Germany, his connections with German mathematicians, and the first English translation of Gottlob Frege’s unpublished letter to Adolph Mayer on Giuseppe Peano’s mathematical logic
Besler Gabriela
Kwartalnik Historii Nauki i Techniki
|
2023
|
T. 68, nr 4
9--28
EN
The article aims to answer whether Gottlob Frege’s letter to Adolph Mayer, dated 8 July 1896, could help German mathematicians get acquainted with Giuseppe Peano’s mathematical work, including his mathematical logic. It is the first publication of this letter in English. At the beginning, I present the main characters of this story. Next, I refer to the letters concerning Peano and his mathematical results. Thus, I show the background of Frege’s letter to Mayer. In the last part, I collect information about Peano’s contacts with German mathematicians - where he was quoted and by whom, who was quoted by Peano, and in which period of his life. I conclude that Peano was known in Germany before Frege wrote to Mayer in 1896. However, the letter could have helped publish five of Peano’s articles in Germany, where Peano’s mathematical logic was hardly known then. Undoubtedly, the letter promoted that knowledge.
PL
Celem artykułu jest odpowiedź na pytanie, czy list Gottloba Fregego do Adolpha Mayera, nadany 8 lipca 1896 r., mógl pomóc niemieckim matematykom zapoznać się z pracami matematycznymi Giuseppego Peana, w tym z jego logiką matematyczną. Jest to pierwsze wydanie tego listu w języku angielskim. Najpierw przedstawiam główne postaci tej historii. Następnie omawiam listy dotyczące Peana i jego wyników matematycznych. W ten sposób pokazuję tło listu Fregego do Mayera. W ostatniej części zbieram informacje o kontaktach Peana z niemieckimi matematykami - gdzie był cytowany i przez kogo, kogo cytował Peano i w którym okresie swojego życia. Kończę z wnioskiem, że Peano był znany w Niemczech zanim Frege napisał do Mayera w 1896 r. List mógł jednak pomóc w wydaniu pięciu artykułów Peana w Niemczech, gdzie jego logika matematyczna była wówczas niemal nieznana. Niewątpliwie list pomógł w szerzeniu tej wiedzy.
3
Content available Simple and flexible way to integrate heterogeneous information systems and their services into the world data system
Nowakowski Grzegorz, Telenyk Sergii, Yefremov Kostiantyn, Khmeliuk Volodymyr
Journal of Automation Mobile Robotics and Intelligent Systems
|
2021
|
Vol. 15, No. 4
76--90
EN
The approach to applications integration for World Data Center (WDC) interdisciplinary scientific investigations is developed in the article. The integration is based on mathematical logic and artificial intelligence. Key elements of the approach – a multilevel system architecture, formal logical system, implementation – are based on intelligent agents interaction. The formal logical system is proposed. The inference method and mechanism of solution tree recovery are elaborated. The implementation of application integration for interdisciplinary scientific research is based on a stack of modern protocols, enabling communication of business processes over the transport layer of the OSI model. Application integration is also based on coordinated models of business processes, for which an integrated set of business applications are designed and realized.
4
Content available remote Logic and Algebra in Unfolded Petri Nets : on a Duality Between Concurrency and Causal Dependence
Bernardinello Luca, Ferigato Carlo, Pomello Lucia
Fundamenta Informaticae
|
2020
|
Vol. 171, nr 1-4
39--56
EN
An orthogonality space is a set endowed with a symmetric and irreflexive binary relation (an orthogonality relation). In a partially ordered set modelling a concurrent process, two such binary relations can be defined: a causal dependence relation and a concurrency relation, and two distinct orthogonality spaces are consequently obtained. When the condition of N-density holds on both these orthogonality spaces, we study the orthomodular poset formed by closed sets defined according to Dacey. We show that the condition originally imposed by Dacey on the orthogonality spaces for obtaining an orthomodular poset from his closed sets is in fact equivalent to N-density. The requirement of N-density was as well fundamental in a previous work on orthogonality spaces with the concurrency relation. Starting from a partially ordered set modelling a concurrent process, we obtain dual results for orthogonality spaces with the causal dependence relation in respect to orthogonality spaces with the concurrency relation.
5
Content available remote Personal Reflections on the Role of Mathematical Logic in Computer Science
Kfoury Assaf
Fundamenta Informaticae
|
2019
|
Vol. 170, nr 1-3
207--221
EN
This article traces in broad strokes the evolution of the intimate relationship between mathematical logic and computer science. The emphasis is on turning points in this relationship, i.e., moments when new directions of research were opened and new connections were established between the two fields. The article is not a comprehensive account and history of the relationship, but a personal perspective of a profoundly changed, and still changing, inter-dependence between two mainstays of the mathematical disciplines.
6
Content available remote The approach to applications integration for world data center interdisciplinary scientific investigations
Nowakowski Grzegorz, Telenyk Sergii, Yefremov Kostiantyn, Khmeliuk Volodymyr
Annals of Computer Science and Information Systems
|
2019
|
Vol. 18
539--545
EN
The approach to applications integration for World Data Center (WDC) interdisciplinary scientific investigations is developed in the article. The integration is based on mathematical logic and artificial intelligence. Key elements of the approach - a multilevel system architecture, formal logical system, implementation - are based on intelligent agents interaction. The formal logical system is proposed. The inference method and mechanism of solution tree recovery are elaborated. The implementation of application integration for interdisciplinary scientific research is based on a stack of modern protocols, enabling communication of business processes over the transport layer of the OSI model. Application integration is also based on coordinated models of business processes, for which an integrated set of business applications are designed and realized.
7
Content available remote SMT-Based Reachability Checking for Bounded Time Petri Nets
Półrola A., Cybula P., Męski A.
Fundamenta Informaticae
|
2014
|
Vol. 135, nr 4
467--482
EN
Time Petri nets by Merlin and Farber are a powerful modelling formalism. However, symbolic model checking methods for them consider in most cases the nets which are 1-safe, i.e., allow the places to contain at most one token. In our paper we present an approach which applies symbolic verification to testing reachability for time Petri nets without this restriction. We deal with the class of bounded nets restricted to disallow multiple enabledness of transitions, and present the method of reachability testing based on a translation into a satisfiability modulo theory (SMT).
8
Content available remote The reception of logic in Poland: 1870‒1920
Woleński J.
Czasopismo Techniczne. Nauki Podstawowe
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2014
|
R. 111, z. 1-NP
245--253
EN
This paper presents the reception of mathematical logic (semantics and methodology of science are entirely omitted, but the foundations of mathematics are included) in Poland in the years 1870–1920. Roughly speaking, Polish logicians, philosophers and mathematicians mainly followed Boole’s algebraic ideas in this period. Logic as shaped by works of Gottlob Frege and Bertrand Russell became known in Poland not earlier than about 1905. The foundations for the subsequent rapid development of logic in Poland in the interwar period were laid in the years 1915–1920. The rise of Polish Mathematical School and its program (the Janiszewski program) played the crucial role in this context. Further details can be found in [8]. This paper uses the material published in [20‒24].
PL
W artykule przedstawiono recepcję logiki matematycznej w Polsce w latach 1870–1920. Polscy logicy, zarówno filozofowie jak i matematycy, kontynuowali algebraiczne idee Boole’a w tym okresie. Logika w stylu Gottloba Fregego i Bertranda Russella stała się znana w Polsce około 1905 r. Podwaliny pod dalszy szybki rozwój logiki w okresie międzywojennym zostały położone w latach 1915–1920. Powstanie Polskiej Szkoły Matematycznej i jej program (program Janiszewskiego) odegrały kluczową rolę w tym kontekście. Dalsze szczegóły można znaleźć w [8, 12]. Niniejszy artykuł korzysta z materiału zawartego w [20‒24].
9
Content available remote On the history of logic in the Russian Empire (1850–1917)
Schumann A.
Czasopismo Techniczne. Nauki Podstawowe
|
2014
|
R. 111, z. 1-NP
185--194
EN
In 1850 a very important decision for the whole history of humanities and social sciences in Russia was made by Nicholas I, the Emperor of Russia: to eliminate the teaching of philosophy in public universities in order to protect the regime from the Enlightenment ideas. Only logic and experimental psychology were permitted, but only if taught by theology professors. On the one hand, this decision caused the development of the Russian theistic philosophy enhanced by modern methodology represented by logic and psychology of that time. On the other hand, investigations in symbolic logic performed mainly at the Kazan University and the Odessa University were a bit marginal. Because of the theistic nature of general logic, from 1850 to 1917 in Russia there was a gap between philosophical and mathematical logics.
PL
W 1850 r. car Rosji Mikołaj I wydał ważny dla nauk humanistycznych w Rosji edykt: wyeliminować nauczanie filozofii w uczelniach publicznych w celu ochrony systemu naukowego od idei Oświecenia. Tylko logika i psychologia eksperymentalna były dozwolone, jeśli prowadzili je profesorowie teologii. Z jednej strony, taka decyzja spowodowała rozwój rosyjskiej filozofii teistycznej wzmocnionej przez nowoczesne metodologie reprezentowane przez logikę i psychologię tamtych czasów. Z drugiej strony, badania w logice symbolicznej prowadzone głównie na uniwersytetach w Kazaniu i Odessie miały charakter marginalny. Ze względu na ogólny charakter teistyczny logiki, w Rosji w latach 1850–1917 nie było związków między logiką filozoficzną i matematyczną.
10
Content available A certain approach to Kripke semantics for normal modal logics
Bryll G., Sochacki R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
13-20
EN
In this paper the authors propose a method of verifying formulae in normal modal logics. In order to show that a formula α is a thesis of a normal modal logic, a set of decomposition rules for any formula is given. These decomposition rules are based on the symbols of assertion and rejection of formulae.
11
Content available remote W-irreducible Lattices
Grygiel J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2005
|
Vol. 10
77--81
EN
A finite lattice is W-irreducible if it cannot be split into two overlapping lattices, one of them being an ideal and the other a filter of the lattice. We give some characterization of finite W-irreducible lattices.
12
Content available remote Some Propositional Calculus Oppositional with Respect to the Intuitionistic Propositional Calculus
Bryll G., Kaptur M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2005
|
Vol. 10
17--23
EN
A fragmentary system of the classical propositional calculus, in which the law C N N αα is valid instead of the law CαN N α, is presented.
13
Content available remote Proof Methods for Corecursive Programs
Gibbons J., Hutton G.
Fundamenta Informaticae
|
2005
|
Vol. 66, nr 4
353--366
EN
Recursion is a well-known and powerful programming technique, with a wide variety of applications. The dual technique of corecursion is less well-known, but is increasingly proving to be just as useful. This article is a tutorial on the four main methods for proving properties of corecursive programs: fixpoint induction, the approximation (or take) lemma, coinduction, and fusion.
14
Content available remote A View on Rough Set Concept Approximations
Bazan J., Nguyen H.S., Szczuka M.
Fundamenta Informaticae
|
2004
|
Vol. 59, nr 2,3
107--118
EN
The concept of approximation is one of the most fundamental in rough set theory. In this work we examine this basic notion as well as its extensions and modifications. The goal is to construct a parameterized approximation mechanism making it possible to develop multi-stage multi-level concept hierarchies that are capable of maintaining acceptable level of imprecision from input to output.
15
Content available remote Wykorzystanie idei odrzucania zdań w procesie dydaktycznym
Bryll G., Wlazłowska-Zając U.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
Vol. 7
106--115
16
Content available remote Rachunek refutacyjny a rachunek dualny
Bryll G., Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
Vol. 7
23--29
17
Content available remote Metoda założeniowa odrzucania wyrażeń dla intuicjonistycznego rachunku zdań i systemu S4 Lewisa
Kostrzycka Z., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
Vol. 7
50--59
18
Content available remote Extensions of the Grzegorczyk Logic Determined by Some Countable Boolean Algebras
Dzik W.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
Vol. 6
8--20
EN
It is shown that a chain of type of w + 1 of modal logics: Tr = Grz + B1 ⊃ Grz + B2 ⊃ Grz + B3 ⊃...⊃ Grz (all of them are extensions of the Grzegorczyk logic Grz), contains all and only such modal logics which can be obtained as sets of formulae that are valid in the Stone spaces of countable superatomic Boolean algebras. Some topological conditions which correspond to the Grzegorczyk logic are presented.
19
Content available remote Aksjomatyzacja rachunku zdaniowego dualnego względem klasycznego implikacyjno-negacyjnego rachunku zdań
Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
Vol. 7
30--36
20
Content available remote Category approach to R L4 - sets
Biegańska T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1998
|
Vol. 4
85-88
EN
In this paper Fm going to investigate the subcategory of the category of sets valued by some Heyting algebra. The notion of a Heyting algebra valued set was introduced by Scott [1] in 1972 in his work a the intuitionistic set theory. The categories of Heyting algebra valued sets were investigated and described by D. Higgs in [3] and [4].
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