Fibring Logics

Front Cover
Clarendon Press, Nov 5, 1998 - Mathematics - 488 pages
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.
 

Contents

An overview of fibred semantics and the combination of logics 11244 5566
1
Logics and their semantics
18
Combining modal logics
39
Intuitionistic modal logics
76
Discussion and comparison with the literature
91
Introducing selffibring
112
Selffibring of predicate logics
124
Selffibring with function symbols
148
Combining temporal logic systems
255
Fibring implication logics
283
Grafting modalities onto substructural implication systems
307
Products of modal logics
327
Fibring intuitionistic logic programs
380
Fibring semantic tableaux
401
Fibring modal tableaux
421
Fibring labelled deductive systems
440

Selffibring of intuitionistic logic
158
Applications of selffibring
175
Conditional implications and nonmonotonic consequence
210
How to make your logic fuzzy
227
Conclusion and discussion
457
Index
473
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