Mechanization of Reasoning in a Historical PerspectiveThis 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. |
Contents
| 11 | |
The Formalization of Arguments | 45 |
Leibnizs Idea of Mechanical Reasoning | 77 |
The English Algebra of Logic in the 19th Century | 129 |
The 20th Century Way to Formalization | 161 |
Mechanized Deduction Systems | 209 |
References | 231 |
| 253 | |
Extended Table of Contents | 261 |
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Mechanization of Reasoning in a Historical Perspective Witold Marciszewski,Roman Murawski Limited preview - 1995 |
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17th century abstract algebra of logic algorithm Analysis of Logic Aristotle arithmetic automated theorem automated theorem proving axioms Begriffsschrift Boole Boole's called Cartesian chapter clause cognitive science combinations combinatorial concepts conjunctive normal form consists data-processing denote Descartes diagrams discussion domain equation example express fact finite formula Frege function Gentzen given Hauptsatz hence Herbrand Hilbert human idea information-processing interpretation introduced Jevons judgement language Leibniz letters logical form logicians Lull Lull's Lullus machine mathematical logic mathematician means mechanization of reasoning method middle term mind model-based Morgan namely natural deduction negation normal form notation objects operations paper Peano philosophical predicate calculus predicate logic premisses prenex normal form Principia problem procedure proof propositional propositional calculus quantifiers relations resolution rules of inference Russell sense sentence sequence Skolem syllogism syllogistic symbols theorem proving theory tion traditional transformation truth universe variables Venn
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Page 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,...