Books in the Oxford Logic Guides series

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.

Topos theory provides an important setting and language for much of mathematical logic and set theory. This book presents a convenient and natural solution to the treatment of geometric morphisms in this setting and shows how this may be applied to topics such as the relative Giraud theorem.

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.

Stewart Shapiro presents a distinctive original view of the foundations of mathematics, arguing that second-order logic has a central role to play in laying these foundations. He gives an accessible account of second-order and higher-order logic, paying special attention to philosophical and historical issues.

'Oxford Logic Guide provides comprehensive coverage of a new research area in algebra and model theory. Model theoretical and group theoretical notions are explained in detail, and almost all the known results in the area are included. Aimed at the needs of the graduate student, there are many exercises (with hints) and carefully chosen examples.

This is a mathematically-oriented advanced textbook in modal logic, a discipline conceived in philosophy and having found applications in mathematics, artificial intelligence, linguistics, and computer science. It presents in a systematic and comprehensive way a wide range of classical and novel methods and results and can be used by a specialist as a reference book.

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.

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.

An up-to-date, systematic account of the fundamental results of the central areas of model theory (a branch of mathematical logic). The fine structure of models of stable theories is the object of the study, and there are applications to classification theory (such as classifying models of undimensional theories).

The text introduces categories and elementary toposes while requiring little mathematical background. It defines the key concepts and gives complete elementary proofs of theorems, including the fundamental theorem of toposes and the sheafification theorem.

'Many-valued Logics' attempts an elementary exposition of the topics connected with logical many-valueness. It provides readers with a stimulating discussion which focuses on the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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.

An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom of choice.

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).

BL Indispensable reference for both the pure logician and the theoretical computer scientistThis long awaited book gives a thorough account of the mathematical foundations of Temporal Logic, one of the most important areas of logic in computer science.

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice.

This is a new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader through the basic mathematical and philosophical concepts. Topics like the Bar Theorem, valuation systems and first-order logic have been revised.

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.

This updated edition offers the reader an introduction to the field, which focuses on Quine's original work. It includes a revised account of the set theories of Church-Oswald and Mitchell, with permutation models and extensions that preserve power sets.