Analysis and synthesis of logics: how to cut and paste reasoning systems

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are providedfor a combined logic to be sound and complete when the original component logics are known to be sound and complete. The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems).First book addressing both composition and decomposition of logics. Tool box for combining and decomposing logics in different guises. Mathematical approach. Several examples in such diverse areas as software specification, knowledgerepresentation, argumentation theory, networks, security protocols and quantum computing. Written by internationally leading researchers in the field of pure and applied logic and philosophy INDICE: Preface. 1. Introductory Overview. 2. Splicing Logics: Syntactic Fibring. 3. Splicing Logics: Semantic Fibring. 4. Heterogenous Fibring. 5. Fibring Non-Truth Functional Logics. 6. Fibring First-Order Logics. 7. Fibring Higher-Order Logics. 8. Modulated Fibring. 9. Splitting Logics. 10. New Trends: Network Fibring. 11. Summing-up and Outlook. Bibliography. Subject Index. Tableof Symbols. List of Figures.

• ISBN: 978-1-4020-6781-5
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 620
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés