Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining-or fibring-systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate. Using this methodology the book discusses ways of obtaining a wide variety of multimodal, modal intuitionistic, modal substructural and fuzzy systems in a uniform way. It also covers self-fibred languages which allow formulae to apply to themselves. The book also studies sufficient conditions for transferring properties of the component logics into properties of the combined system.
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
Reviews for Fibring Logics
<br> 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<br>