Sheaves, Games, and Model Completions

A Categorical Approach to Nonclassical Propositional Logics

Silvio Ghilardi, M. Zawadowski (Autoren)

Buch | Softcover

245 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2002
Springer (Verlag)
978-90-481-6036-5 (ISBN)

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This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic through the so-called 'Pitts' quantifiers' or 'bisimulation quantifiers'. On the other hand, the book develops a large number of topics concerning the categorical structure of finitely presented al gebras, with related applications to propositional logics, both standard (like Beth's theorems) and new (like effectiveness of internal equivalence relations, projectivity and definability of dual connectives such as difference). A special emphasis is put on sheaf representation, showing that much of the nice categor ical structure of finitely presented algebras is in fact only a restriction of natural structure in sheaves. Applications to the theory of classifying toposes are also covered, yielding new examples. The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics. 1.

1. Introduction.- 2. Preliminary Notions.- 3. Model Completions.- 4. Heyting Algebras.- 5. Duality for Modal Algebras.- 6. Model Completions in Modal Logic.- 7. Algebraically Closed Models.- 8. Open Problems.- 9. Appendix.- References.- Glossary of Notation.

Reihe/Serie	Trends in Logic ; 14
Zusatzinfo	IX, 245 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	160 x 240 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
	Geisteswissenschaften ► Philosophie ► Logik
	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	90-481-6036-7 / 9048160367
ISBN-13	978-90-481-6036-5 / 9789048160365
Zustand	Neuware