Wyniki wyszukiwania - Biblioteka Nauki

1

Personal Reflections on the Role of Mathematical Logic in Computer Science

100%

Kfoury A.

Fundamenta Informaticae

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2019

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tom 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.

2

Jana Franciszka Drewnowskiego filozofia matematyki i logiki

86%

Murawski R.

Studia Philosophiae Christianae

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2019

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tom 55

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nr 2

87-102

EN

This paper illustrates and critically evaluates Jan Franciszek Drewnowski’s philosophical views on mathematics and logic. It is based on four sources. The main source is his “Zarys programu filozoficznego” (“Outline of a Philosophical Program”) (1934). Further sources include two of Drewnowski’s papers, “Stosowanie logiki symbolicznej w filozofii” (“Application of symbolic logic in philosophy”) (1965) and “Uwagi o stosowaniu logiki symbolicznej” (“Remarks on applying symbolic logic”) (1967), as well as fragments from his diary. This paper aims to show how Drewnowski understood mathematics and mathematical theories, how he conceived logic and its role in science, as well as to what extent he was familiar with contemporary achievements in mathematical logic and the foundations of mathematics and his awareness of their relevance for the philosophy of mathematics.

PL

Praca poświęcona jest prezentacji i krytycznej ocenie poglądów filozoficznych Jana Franciszka Drewnowskiego na matematykę i logikę. Podstawą rozważań są cztery źródła. Podstawowym źródłem jest Drewnowskiego "Zarys programu filozoficznego" (1934), dalej dwa artykuły, a mianowicie "Stosowanie logiki symbolicznej w filozofii" (1965) oraz "Uwagi o stosowaniu logiki symbolicznej" (1967), w końcu fragmenty dziennika. Pokazuje się w niej, jak Drewnowski rozumiał matematykę i teorie matematyczne, jak widział logikę i jej rolę w nauce oraz na ile był zaznajomiony ze współczesnymi osiągnięciami w zakresie logiki matematycznej i podstaw matematyki oraz z ich konsekwencjami dla filozofii matematyki.

3

The Proslogion: Philosophy and Logic

72%

Testi C. , Casarosa M.

Edukacja Filozoficzna

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2022

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nr 73

79-121

EN

This article proposes an interpretation of St Anselm’s Proslogion that highlights its overall structure and theoretical core. The analysis is conducted in two stages: (a) discussion of the text and its previous interpretations in order to clarify Anselm’s premises and reasoning; (b) formal analysis of the arguments through symbolic logic, and comparison with other ontological arguments. More precisely, we describe a first-order theory corresponding to our interpretation of Anselm’s commitments and show that his conclusions follow from these axioms. The theses that this study will defend are the following: (a) the unum argumentum applies only to “id quo maius cogitari nequit” and not to other similar concepts, such as that of “most perfect being”; (b) the treatise has an overall unity that has an ascending trend; (c) our original formalization of the unum argumentum not only captures the essence of the Proslogion, but also clarifies some features of conceivability.

PL

Artykuł ten przedstawia interpretację Proslogionu św. Anzelma, która ukazuje jego strukturę oraz teoretyczny rdzeń. Analiza została przeprowadzona w dwóch etapach: (1) dyskusja dotycząca tekstu i jego dotychczasowych interpretacji, służąca rozjaśnieniu przesłanek, na których bazuje Anzelm, oraz jego rozumowania; (b) formalna analiza argumentacji z użyciem logiki symbolicznej i porównanie jej z innymi dowodami ontologicznymi. Precyzyjnie rzecz ujmując, opisujemy teorię pierwszego rzędu odpowiadającą naszej interpretacji założeń Anzelma i pokazujemy, że jego wnioski wynikają z owych aksjomatów. Niniejsze studium broni następujących tez: (1) unum argumentum ma zastosowanie tylko do „id quo maius cogitari nequit”, a nie do innych podobnych pojęć, takich jak „byt najdoskonalszy”; (b) traktat jest spójny i charakteryzuje się jednością z tendencją wzrastającą; (c) nasza oryginalna formalizacja unum argumentum nie tylko uchwytuje istotę Proslogionu, lecz także rozjaśnia pewne cechy pojmowalności.

4

The Computational and Pragmatic Approach to the Dynamics of Science

58%

Marciszewski W.

Filozofia i Nauka

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2020

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tom 8/1

31-67

EN

Sciencemeans here mathematics and those empirical disciplines which avail themselves of mathematical models. The pragmaticapproachis conceived in Karl R. Popper’s The Logic of Scientific Discovery(p.276) sense: a logical appraisal of the success of a theory amounts to the appraisal of its corroboration. This kind of appraisal is exemplified in section 6 by a case study—on how Isaac Newton justified his theory of gravitation. The computationalapproach in problem-solving processes consists in considering them in terms of computability: either as being performed according to a model of computation in a narrower sense, e.g., the Turing machine, or in a wider perspective—of machines associated with a non-mechanical device called “oracle”by Alan Turing (1939). Oracle can be interpreted as computer-theoretic representation of intuitionor invention. Computational approach in an-other sense means considering problem-solving processes in terms of logical gates, supposed to be a physical basis for solving problems with a reasoning.Pragmatic rationalismabout science, seen at the background of classical ration-alism (Descartes, Gottfried Leibniz etc.), claims that any scientific idea, either in empirical theories or in mathematics, should be checked through applications to problem-solving processes. Both the versions claim the existence of abstract objects, available to intellectual intuition. The difference concerns the dynamics of science: (i) the classical rationalism regards science as a stationary system that does not need improvements after having reached an optimal state, while (ii) the pragmatical ver-sion conceives science as evolving dynamically due to fertile interactions between creative intuitions, or inventions, with mechanical procedures.The dynamics of science is featured with various models, like Derek J.de Solla Price’sexponential and Thomas Kuhn’s paradigm model (the most familiar instanc-es). This essay suggests considering Turing’s idea of oracle as a complementary model to explain most adequately, in terms of exceptional inventiveness, the dynam-ics of mathematics and mathematizable empirical sciences.

5

Możliwości zastosowania tablic decyzyjnych w inżynierii projektowania konstrukcyjnego i technologicznego

58%

Partyka M. A. , Paszek A.

Napędy i Sterowanie

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2017

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tom R. 19, nr 10

108--116

PL

W pracy przedstawiono możliwości zastosowania tablic decyzyjnych w inżynierii projektowania w zakresie konstrukcji i technologii. Scharakteryzowano podstawową budowę i własności tablic decyzyjnych w przetwarzaniu informacji bazującej na regułach projektowania. Porównano klasyczne oraz wielowartościowe tablice decyzyjne wspomagające obliczenia cieplne zbiornika ożebrowanego. Pokazano przykłady opracowań tablic decyzyjnych stosowanych w diagnostyce łożyska hydrodynamicznego oraz w opisie stanów automatu skończonego. W obszarze projektowania technologicznego zaprezentowano opracowanie klasycznej tablicy decyzyjnej w projektowaniu obróbki tłoczysk oraz modalną tablicę decyzyjną w projektowaniu półfabrykatów dla produkcji dławnic siłowników hydraulicznych.

EN

The text has been described the basic structure of decision tables in date processing based on design rules. We compared classic and multiple-valued decision tables supporting the thermal calculations of hydraulic tank. There are shown examples of decision solutions in diagnostics of hydrodynamic bearing and in the description of a finite automata. Furthermore, it has been shown that it is possible to build the classic decision table in the design of piston rod machining. The article describes modal decision tables in the design of semi-finished products for the production of hydraulic cylinder glands.

6

The Computational and Pragmatic Approach to the Dynamics of Science

58%

Marciszewski W.

Filozofia i Nauka

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2020

|

tom 8

|

nr 1

31-67

EN

Science means here mathematics and those empirical disciplines which avail themselves of mathematical models. The pragmatic approach is conceived in Karl R. Popper’s The Logic of Scientific Discovery (p. 276) sense: a logical appraisal of the success of a theory amounts to the appraisal of its corroboration. This kind of appraisal is exemplified in section 6 by a case study-on how Isaac Newton justified his theory of gravitation. The computational approach in problem-solving processes consists in considering them in terms of computability: either as being performed according to a model of computation in a narrower sense, e.g., the Turing machine, or in a wider perspective-of machines associated with a non-mechanical device called “oracle” by Alan Turing (1939). Oracle can be interpreted as computertheoretic representation of intuition or invention. Computational approach in another sense means considering problem-solving processes in terms of logical gates, supposed to be a physical basis for solving problems with a reasoning. Pragmatic rationalism about science, seen at the background of classical rationalism (Descartes, Gottfried Leibniz etc.), claims that any scientific idea, either in empirical theories or in mathematics, should be checked through applications to problem-solving processes. Both the versions claim the existence of abstract objects, available to intellectual intuition. The difference concerns the dynamics of science: (i) the classical rationalism regards science as a stationary system that does not need improvements after having reached an optimal state, while (ii) the pragmatical version conceives science as evolving dynamically due to fertile interactions between creative intuitions, or inventions, with mechanical procedures. The dynamics of science is featured with various models, like Derek J. de Solla Price’s exponential and Thomas Kuhn’s paradigm model (the most familiar instances). This essay suggests considering Turing’s idea of oracle as a complementary model to explain most adequately, in terms of exceptional inventiveness, the dynamics of mathematics and mathematizable empirical sciences.