Mechanization of Reasoning in a Historical Perspective / / Witold Marciszewski, Roman Murawski.

• VerfasserIn: Marciszewski, Witold,; Murawski, Roman,
• TeilnehmendeR: Murawski, Roman,
• Place / Publishing House: Leiden : : BRILL,, 1995.
• Year of Publication: 1995
• Edition: 1st ed.
• Language: English
• Series: Poznań Studies in the Philosophy of the Sciences and the Humanities Series
• Physical Description: 1 online resource.

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 re...

Table of Contents

• Intro
• Title Page
• Copyright Page
• Acknowledgements
• Table of Contents
• 1. From the Mechanization of Reasoning to a Study of Human Intelligence
• 1.1. Von Neumann's project related to cognitive science
• 1.2. The Leibniz-style Cybernetic Universe
• 1.3. Information-processing through data-processing
• 1.4. Intelligence and model-based reasoning
• 2. The Formalization of Arguments in the Middle Ages
• 2.1. The contention of the present chapter
• 2.2. Heuristic algorithms in the Middle Ages
• 2.3. The role of Lull and Lullism
• 3. Leibniz's Idea of Mechanical Reasoning at the Historical Background
• 3.1. An interaction between logic and mathematics
• 3.2. The Renaissance reformism and intuitionism in logic
• 3.3. Leibniz on the mechanization of arguments
• 4. Between Leibniz and Boole: Towards the Algebraization of Logic
• 4.1. Preliminary remarks
• 4.2. Leibniz's direct successors
• 4.3. The work of J. H. Lambert
• 5. The English Algebra of Logic in the 19th Century
• 5.1. A. De Morgan's syllogistic and the theory of relations
• 5.2. G. Boole and his algebra of logic
• 5.3. The Logical works of Jevons
• 5.4. J. Venn and logical diagrams
• 5.5. Conclusions
• 6. The 20th Century Way to Formalization and Mechanization
• 6.1. Introduction
• 6.2. G. Peano - symbolic language and the axiomatization of mathematics
• 6.3. G. Frege and the idea of a formal system
• 6.4. B. Russell and the fulfillment of Peano's and Frege's projects
• 6.5. Skolemization
• 6.6. D. Hilbert and his program
• 6.7. J. Herbrand
• 6.8. G. Gentzen and natural deduction
• 6.9. Semantic and analytic tableaux
• 6.10. Conclusions
• 7. Mechanized Deduction Systems
• 7.1. Introduction
• 7.2. First mechanized deduction systems
• 7.3. Unification and resolution
• 7.4. Further development of mechanized deduction systems after 1965.
• 7.5. Final remarks
• References
• Index of Subjects
• Index of Names
• Extended Table of Contents.