Mechanization of Reasoning in a Historical Perspective
This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being.
The study which resulted in this volume was carried out in the Historical Section of the research project Logical Systems and Algorithms for Automatic Testing of Reasoning, 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia l ystok Branch of the University of Warsaw, and supported by the Ministry of Education (some of its results are reported in (Srzednicki (Ed.) 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE (Multi-Sorted first-order logic with Equality, reported in (Marciszewski 1994a)) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration.
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Sadly quite disappointing. Touches on all the right subject, but quality is extremely mixed. Comes up with at least three different spellings of Russell. Przeczytaj pełną recenzję
The Formalization of Arguments
Leibnizs Idea of Mechanical Reasoning
The English Algebra of Logic in the 19th Century
The 20th Century Way to Formalization
Mechanized Deduction Systems
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17th century abstract according algebra algorithm analysis approach arguments arithmetic authors axioms Boole calculus called century chapter clause combinations concepts conclusion consequence considered consists constructed contains context deduction definition denote described discussion elements equation equivalence example existence express fact formal formula Frege function given hence Hilbert human idea important included inference instance interpretation introduced known language laws Leibniz letters logic logicians Lull Lull's machine mathematics means mechanization mentioned method middle mind Morgan namely natural Note objects obtain operations Peano philosophical physical possible precise predicate present problem procedure proof propositional prove question reasoning refer relations represented resolution rules Russell sense sentence signs statements step syllogism syllogistic symbols theorem theory things thought tion traditional transformation true truth universe variables various write
Strona 13 - At this point it only furnishes another illustration of the situation outlined earlier. There is an equivalence between logical principles and their embodiment in a neural network, and while in the simpler cases the principles might furnish a simplified expression of the network, it is quite possible that in cases of extreme complexity the reverse is true. All of this does not alter my belief that a new, essentially logical, theory is called for in order to understand high-complication automata and,...