Universal Logic: An Anthology : From Paul Hertz to Dov Gabbay

ISBN-13: 9783034601443 / Angielski / Miękka / 2012 / 410 str.

Jean-Yves Beziau

Opis

A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and influence.

Recenzje

From the reviews:

“The quest for common ground in the expression of logical statements--regardless of the given syntax, semantics, or grammar--has taken the best efforts of notable logicians throughout the 20th century. This book gathers a collection of some of the most notable of their works. Its structure is chronological … . I highly recommend this book to logicians, mathematicians working on provability theory, and software engineers.” (Arturo Ortiz-Tapia, ACM Computing Reviews, July, 2012)

Spis treści

1. Paul Hertz (1922), «Über Axiomensysteme für beliebige Satzsysteme, Teil. 1» presented by Javier Legris // 2. Paul Bernays (1926), «Axiomatische Untersuchung des Aussagenkalküls des Principia Mathematica» presented by Walter Carnielli // 3. Alfred Tarski (1928), «Remarques sur les notions fondamentales de la méthodologie des mathématiques», presented by Stan Surma and Jan Zygmunt // 4. Kurt Gödel (1933), «Eine Interpretation des intuitionistischen Aussagenkalküls» presented by presented by Itala D'Ottavianao and Hercules Feitosa// 5. Louis Rougier (1941), «The relativity of logic» presented by Mathieu Marion // 6. Haskell B. Curry (1952), Leçons de logique algébrique (Translation of extracts) presented by Johnatan Seldin // 7. Jerzy Los and Ronam Suszko (1958), «Remarks on sentential logics» presented by Jan Zygmunt // 8. Saul Kripke (1963), «Semantical Considerations on Modal Logic» presented by Johan van Benthem // 9. Jean Porte (1965), Recherches sur la théorie générale des systèmes formels et sur les systèmes connectifs (Translation of extracts) presented by Marcel Guillaume // 10. Per Lindström (1969), « On extensions of elementary logic » presented by Jouko Väänänen // 11. Stephen L.Bloom, Donald J.Brown et Roman Suszko (1970), «Some theorems on abstract logics» presented by Ramon Jansana // 12. Dana Scott (1974), «Completeness and axiomatizability in many-valued logic» presented by Lloyd Humberstone // 13. Joseph Goguen and Rod Burstall (1984), «Introducing institutions» presented by Razvan Diaconescu // 14. Andrea Loparic and Newton da Costa (1984), «Paraconsistency, paracompleteness and valuations» presented by Jean-Yves Béziau // 15. Dov Gabbay, «Fibred Semantics and the Weaving of Logics, Part 1: Modal and Intuitionistic logic» (extracts) presented by Amilcar Sernadas and Carlos Caleiro

O autorze

Jean-Yves Béziau ist Professor und Forscher des brasilianischen Forschungrsrates -CNPq - der nationalen Universität in Ceara, Brasilien. Béziau ist französischer und schweizerischer Doppelbürger. Er spricht fliessend Englisch, Portugiesisch und muttersprachlich Französisch und hat in allen drei Sprachen Werke veröffentlicht. Als ehemaliger Student (und häufig als Mitarbeiter ) von Newton da Costa, arbeitet er im Gebiet der Logik - besonders in paraconsistenter Logik und allgemeine Logik. Er wurde an der Universität von São Paulo in Philosophie und an der Universität von Paris in Logik und Grundlagen in Computerwissenschaften promoviert. Béziau ist Chefeditor und Gründer der Zeitung Logica Universalis und der Buchreihe Studies in Universal Logic.