Fibring LogicsModern 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
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 |
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Common terms and phrases
actual world algebra applied arbitrary assignment assume atomic q axiomatisation axioms binary binary relation C₁ calculus canonical model classical logic clause completeness theorem connectives consequence relation consider consistent construction corresponding countermodel defined Definition denote disjunction dovetailed equivalent evaluation example extension F₁ fibred model fibred semantics fibring function finite first-order following holds formula frame free logic free variables function F function symbols fuzzy Gabbay generalised Hence implies intuitionistic logic Kripke frames Kripke model Kripke semantics L₁ L1 and L2 labels language Lemma logic programming logic system modal logic monadic monotonic multimodal logic n-modal non-monotonic notation notion obtained operators possible world predicate logic proof properties propositional quantifiers restricted rules satisfies Section self-fibred subset substitution substructural logics temporal logic temporalisation theory transitive translation truth value two-dimensional unary predicate valid wffs
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