Bøker i Oxford Logic Guides-serien

This research text presents and uses a novel methodology for reasoning about actions and change. The work described here uses a systematic methodology for identifying the exact range of applicability of a given logic. This book is destined to become a necessary source of reference for researchers in knowledge representation, cognitive robotics, and intelligent control in the future.

Setting a new direction in research in the subject, this book presents a new view of cardinal arithmetic, one of the central issues in set theory. Focusing on cofinalities rather than cardinalities, new results are obtained and published here for the first time.

This monograph is on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.

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.

Mathematical logic is an area of interest to workers in philosophy and computer science as well as mathematics. This book, the companion to an already successful volume by the same authors, deals with an area of logic of interest in computer science, which considers the particularly rich and complex effects of time.

In 1931, Princeton mathematician Kurt Godel startled the scientific world with his 'Theorem of Undecidability', which showed that some statements in mathematics are inherently 'undecidable'. This volume of the 'Oxford Logic Guides' is a sequel to Smullyan's Godel's 'Incompleteness Theorems' (Oxford Logic Guides No. 19, 1992).

This book principally concerns the area of "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. This includes an open problem list of 7 fundamental and 39 technical questions together with a bibliography of references.

A great variety of logical systems arise in mathematical logic and computer science. This is a new systematic study of the principles behind such logics. The technical work is illuminated by information about its historical and philosophical context.

Martin-Lof Type Theory is both an important and practical formalization and a focus for a charismatic view of the foundations of mathematics. This volume, including one of Per Martin-Lof's earliest papers, celebrates the 25th anniversary of the birth of the subject.