Modern applications of logic in mathematics, computer science, and linguistics require combined systems composed of different types of logic working together. In this book the author offers a basic methodology for combining--or fibring--systems. The technique shows how to break complex systems into simple components which can be easily manipulated and recombined.

Fibring Logics (Oxford Logic Guides)

Computers & Technology

Gabbay, Dov. M.

Programming

Clarendon Press

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. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigious world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of Intuitionism (Second Edition), J.M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P.T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof, Theory, Semantics and Control.

Interpolation and Definability: Modal and Intuitionistic Logic (Oxford Logic Guides)

Science & Math

Maksimova, Larisa

Mathematics

Logic is now widely recognized to be one of the foundational disciplines of computing with applications reaching almost every aspect of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of Logic in Artificial Intelligence and Logic Programming is a multi-volume work covering all major areas of application of logic to AI and logic programming. Each volume features a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying themes in the various areas. Volumes 1 and 2 present the logical foundations and deduction methodologies extensively used in AI. Volumes 3 and 4 cover reasoning, and Volume 5 details logic programming. The chapters, which in many cases are of monograph length and scope, emphasize possible unifying themes and are written by internationally renowned researchers. Students and researchers of artificial intelligence, computer science, and logic will find this landmark reference invaluable to their work.

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 2: Deduction Methodologies

Hogger, C. J.

Robinson, J. A.

Computer Science

Logic is now widely recognized to be one of the foundational disciplines of computing with applications reaching almost every aspect of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of Logic in Artificial Intelligence and Logic Programming is a multi-volume work covering all major areas of application of logic to AI and logic programming. Each volume features a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying themes in various areas. Volumes 1 and 2 present the logical foundations and deduction methodologies extensively used in AI. Volumes 3 and 4 cover reasoning, and Volume 5 details logic programming. The chapters, which in many cases are of monograph length and scope, emphasize possible unifying themes and are written by internationally known researchers. Students and researchers of artificial intelligence, computer science, and logic will find this landmark reference invaluable to their work.

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning

This is the second volume in a series of well-respected works in temporal science and is by the same authors as the first. Volume one dealt primarily with basic concepts and methods, volume two discuses the more applicable aspects of temporal logics. The first four chapters continue the more theoretical presentations from volume one, covering automata, branching time and labelled deduction. The rest of the book is devoted to discussions of temporal databases, temporal execution and programming, actions and planning. With its inclusion of cutting-edge results and unifying methodologies, this book, and its companion are an indispensable reference for both the pure logician and the theoretical computer scientist.

Temporal Logic: Mathematical Foundations and Computational Aspects: Volume 2

Reynolds, Mark A.

Finger, Marcelo

Oxford University Press

This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and unifying methodologies, this book is an indispensable reference for both the pure logician and the theoretical computer scientist.

Temporal Logic: Mathematical Foundations and Computational AspectsVolume 1 (Oxford Logic Guides)

Reynolds, Mark

Hodkinson, Ian

The dramatic increase in research in recent years shows that logic is now widely recognized as one of the foundational disciplines of computing and has found applications in virtually all aspects of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of Logic in Artificial Intelligence and Logic Programming was created in response to the growing need for an in-depth survey of these applications, and as a result is a unique and invaluable reference source. The Handbook comprises five volumes, each an in-depth overview of one of the major topics in this area. It is the result of years of cooperative effort by internationally renowned researchers in the field, and will no doubt be the standard reference work in AI for years to come. Volume IV covers, among other subjects, epistemic reasoning, time and change for AI, and temporal nonmonotonic reasoning.

Handbook of Logic in Artificial Intelligence and Logic Programming

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.

Labelled Deductive Systems (Oxford Logic Guides)

Politics & Social Sciences

Philosophy

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. 
The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. 
The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments.

Handbook of the Logic of Argument and Inference: The Turn Towards the Practical (Volume 1) (Studies in Logic and Practical Reasoning, Volume 1)

WOODS, JOHN

Johnson, R.H.

Ohlbach, H.J.

North-Holland

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.
 To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.
 We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.
 The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.
 The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.
 Key Features:
 • Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science
 • Written by internationally leading researchers in the field of pure and applied logic
 • Combines mathematical theory of modal logic and applications in artificial intelligence and computer science
 • Numerous open problems for further research
 • Well illustrated with pictures and tables

Many-Dimensional Modal Logics: Theory and Applications (Volume 148) (Studies in Logic and the Foundations of Mathematics, Volume 148)

Zakharyaschev, M

Wolter, F.

Kurucz, A.

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