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-syste…
Change, Choice and Inference develops logical theories that are necessary both for the understanding of adaptable human reasoning and for the design of intelligent systems. The book shows that reasoning processes - the drawing on inferences and chan…
Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, phi…
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of top…
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 c…
Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, t…
This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. Issuing…
Techniques for reasoning about actions an change in the physical world is one of the classical research topics in artificial intelligence. It is motivated by the needs of autonomous robots which must be able to anticipate their immediate future, to…
Now in it's fourth edition, this classic work on logic presents the student with a clear, concise introduction to the subject of logic and its apllications. The first part of the book introduces the concepts and principles which make up the elements…
This is the second volume of this respected work in temporal logic. Whereas volume 1 dealt primarily with basic concepts and methods, volume 2 discusses the more applicable aspects of temporal logics. The first four chapters continue the more theore…
This book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian…
Logic languages are free from the ambiguities of natural languages, and are therefore specially suited for use in computing. Model theory is the branch of mathematical logic which concerns the relationship between mathematical structures and logic l…
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of…
This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these eme…
For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators - `like it is necessary' in philosophy…
Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos which allows a topos to be regarded as a category of sets. This enables a fruitful…
The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a…
This book is a specialized monograph 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 pr…
Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restric…
Model theory, a major branch of mathematical logic, plays a key role connecting logic and other areas of mathematics such as algebra, geometry, analysis, and combinatorics. Simplicity theory, a subject of model theory, studies a class of mathematica…
The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to tru…
The main purpose of this book is to present a unified treatment of fixed points as they occur in Gödel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material…
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas s…
This book is an exposition of the central features of one of the most developed and sophisticated parts of modern model theory. Geometric stability theory studies the fine structure of models of stable theories. An ever present theme is the existenc…
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this…
This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas by the notion of structured families of labelled formulas, the labels having algebraic structure. This simp…
Nonstandard models of arithmetic are of interest to mathematicians through the presence of infinite (or nonstandard) integers and the various properties they inherit from the finite integers. Since their introduction in the 1930s (by Skolem and Göde…
This 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. The book, which consists of fifteen chapters, moves on from giving a solid introduction…
It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to name but a few - which have originated in the areas of mathematical log…
This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic,…
This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and…
This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical con…
Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically solved), it was thought to be essentially solved by the independence resu…
The book is devoted to the theory of groups of finite Morley rank. These groups arise in model theory and generalize the concept of algebraic groups over algebraically closed fields. The book contains almost all the known results in the subject. Try…