Labelled Deductive Systems Volume 1 [Hardcover]

This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.

1. What is a Logical System?
2. Introducing Labelled Deductive Systems
3. Algebraic LDS
4. General LDS
5. Resource Logics
6. Translation of LDS
7. LDS Formulation
8. Curry-Howard Interpretation
9. Structured Consequence Relations
10. Labelled Analytic Deduction
11. Abduction in Labelled Deductive Systems

The book presents the formal machinery of LDSs (Labelled deductive systems): proof theory, semantics, and algebraic LDSs, with many examples: modal and tense logics, fuzzy and many-valued logics, linear and relevant logics, nonmonotonic logic, etc. . . .this book will be of great interest for anyone who wants to grasp, together with a number of formal techniques, a multiplicity of logical systems, mostly related to computer science and artificial intelligence. --Mathematical Reviews