Fibring Logics [Hardcover]

Modern applications of logic in mathematics, computer science, and linguistics require combined systems composed of different types of logic working together. In this book the author offers a basic methodology for combining--or fibring--systems. The technique shows how to break complex systems into simple components which can be easily manipulated and recombined.

1. An overview
2. Logics and their semantics
3. Combining modal logics
4. Intuitionistic modal logics
5. Comparison with literature
6. Introducing self-fibring
7. Self-fibring of predicate logics
8. Self-fibring with function systems
9. Self-fibring of intuitionistic logic
10. Applications of self-fibring
11. Conditional implication
12. How to make your logic fuzzy
13. Combing temporal logic systems
14. Grafting modalities
15. Fibred tableaux

The mechanism of fibring logics can be understood as a methodology which permits one to apply idiosyncratic properties of one given logic (propositional or modal, for instance) to other logics, creating hybrid systems for the sake of purely theoretical interests, or as suggested in several places in this book, directed to applications. The reader can appreciate the difficulties of a still elusive theory of fibring. Although with totally distinct backgrounds, the ideas of fibring, on the one hand, and splitting and splicing, on the other, seem to be complementary processes in the realm of logical systems whose relationships would contribute to the still to be determined general theory of combination of logics. This book is a good contribution in that direction. - Walter Carnielli,Mathematical Reviews, 2000