Mechanization of Reasoning in a Historical Perspective


Volume Editors: Witold Marciszewski and Roman Murawski
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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Acknowledgements. 1. From the Mechanization of Reasoning to a Study of Human Intelligence. Von Neumann's project related to cognitive science. The Leibniz-style Cybernetic Universe. Information-processing through data-processing. Intelligence and model-based reasoning. 2. The Formalization of Arguments in the Middle Ages. The contention of the present chapter. Heuristic algorithms in the Middle Ages. The role of Lull and Lullism. 3. Leibniz's Idea of Mechanical Reasoning at the Historical Background. An interaction between logic and mathematics. The Renaissance reformism and intuitionism in logic. Leibniz on the mechanization of arguments. 4. Between Leibniz and Boole: Towards the Algebraization of Logic. Preliminary remarks. Leibniz's direct successors. The work of J.H. Lambert. 5. The English Algebra of Logic in the 19th Century. A. De Morgan's syllogistic and the theory of relations. G. Boole and his algebra of logic. The Logical works of Jevons. J. Venn and logical diagrams. Conclusions. 6. The 20th Century Way to Formalization and Mechanization. Introduction. G. Peano — symbolic language and the axiomatization of mathematics. G. Frege and the idea of a formal system. B. Russell and the fulfillment of Peano's and Frege's projects. Skolemization. D. Hilbert and his program. J. Herbrand. G. Gentzen and natural deduction. Semantic and analytic tableaux. Conclusions. 7. Mechanized Deduction Systems. Introduction. First mechanized deduction systems. Unification and resolution. Further development of mechanized deduction systems after 1965. Final remarks. References. Index of Subjects. Index of Names. Extended .