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This book introduces a new unifying framework for logics which makes it particularly suitable for applications. It develops its general theory and illustrates it with applications in logic, computer science, artificial intelligence, and philosophy.

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.

Logic languages are used in computing. Model theory is the mathematical logic which concerns the relationship between mathematical structures and logic languages. The text includes historical information before each topic is introduced. The motivation of the subject and the proofs are explained.

A monograph on the interface of computational complexity and randomness of sets of natural numbers.

BL An introduction to the topic - pitched at an elementary level This Oxford Logic Guide presents a unified treatment of fixed points, self-reference, and diagonalization as they occur in Goedel's incompleteness proofs, recursion theory, combinatory logics, semantics, and metamathematics. There is also a presentation of new results - partly in these areas, but mostly in their synthesis.

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

Change, Choice and Inference unifies lively and significant strands of research in logic, philosophy, economics and artificial intelligence.

Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.