C. J. van Rijsbergen – författare

This book is a complete account of the predicate transformation calculus semantics of sequential programs, including repetitions, recursive procedures, computational induction and unbounded nondeterminacy. Predicate transformation semantics are the best specification method for the development of correct and well-structured computer programs. The author develops this theory to a greater depth than has been achieved before, and describes it in a way that makes it readily compatible with programming rules for partial and total correctness of repetitions and recursive procedures, supplies new rules for proving incorrectness, and a stronger rule for proving that two programs satisfy the same specifications. Finally, the semantics are extended so that non-terminating programs can be specified as well. This will be essential reading for all computer scientists working in specification and verification of programs.

The author presents a theory of concurrent processes where three different semantic description methods that are usually studied in isolation are brought together. Petri nets describe processes as concurrent and interacting machines; algebraic process terms describe processes as abstract concurrent processes; and logical formulas specify the intended communication behaviour of processes. At the heart of this theory are two sets of transformation rules for the top-down design of concurrent processes. The first set can be used to transform stepwise logical formulas into process terms, whilst process terms can be transformed into Petri nets by the second set. These rules are based on novel techniques for the operational and denotational semantics of concurrent processes. Various results and relationships between nets, terms and formulas starting with formulas and illustrated by examples. The use of transformations is demonstrated in a series of case studies, and the author also identifies directions for research.

The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequently the ability to specify code and verify program correctness can be improved. Two developments are needed, the first of which introduces the binding time distinction into the lambda calculus, in a manner analogous with the introduction of types into the untyped lambda calculus. Methods are also presented for introducing combinators for run-time. The second concerns the interpretation of the resulting language, which is known as the mixed lambda-calculus and combinatory logic. The notion of 'parametrized semantics' is used to describe code generation and abstract interpretation. The code generation is for a simple abstract machine designed for the purpose; it is close to the categorical abstract machine. The abstract interpretation focuses on a strictness analysis that generalises Wadler's analysis for lists.

Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses.

Petri nets are a popular and powerful formal model for the analysis and modelling of concurrent systems, and a rich theory has developed around them. Petri nets are taught to undergraduates, and also used by industrial practitioners. This book focuses on a particular class of petri nets, free choice petri nets, which play a central role in the theory. The text is very clearly organised, with every notion carefully explained and every result proved. Clear exposition is given for place invariants, siphons, traps and many other important analysis techniques. The material is organised along the lines of a course book, and each chapter contains numerous exercises, making this book ideal for graduate students and research workers alike.

This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycles and intensionality. The resulting synthesis serves as a logical foundation for grammars, logic programming and constraint-based reasoning systems. A logical perspective is adopted which employs an attribute-value description language along with complete equational axiomatizations of the various systems of feature structures. At the same time, efficiency concerns are kept in mind and complexity and representability results are provided. The application of feature structures to phrase structure grammars is described and completeness results are shown for standard evaluation strategies. Definite clause logic programs are treated as a special case of phrase structure grammars. Constraint systems are introduced and an enumeration technique is developed for solving arbitrary attribute-value logic constraints. This book, with its innovative approach to data structure, will be essential reading for researchers in computational linguistics, logic programming and knowledge representation. Its self-contained presentation makes it flexible enough to serve as both a research tool and a text book.

Declarative programs consist of mathematical functions and relations and are amenable to formal specification and verification, since the methods of logic and proof can be applied to the programs in a well-defined manner. Here Dr Padawitz emphasizes verification based on logical inference rules, i.e. deduction (in contrast with model-theoretic approaches, deductive methods can be automated to some extent). His treatment of the subject differs from others in that he tries to capture the actual styles and applications of programming; neither too general with respect to the underlying logic, nor too restrictive for the practice of programming. He generalizes and unifies results from classical theorem-proving and term rewriting to provide proof methods tailored to declarative program synthesis and verification. Detailed examples accompany the development of the methods, whose use is supported by a documented prototyping system. The book can be used for graduate courses or as a reference for researchers in formal methods, theorem-proving and declarative languages.

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject and formalizing within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy and computer science as an account of how mathematics and artificial intelligence can complement and enrich each other.

This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.

Artificial intelligence has recently turned to formal logic in the search for powerful yet well-behaved knowledge representation languages. This book covers the background of classical logic, including the major meta-theorems, and the state of the art in theorem proving including Bibel's connection method. Also covered are the advanced adaptations of classical logic now being used in artificial intelligence - temporal and modal logics, reason maintenance and intensional logic. First published in 1988, the book covers a wider range of topics than the currently available books in this area, and is more directly aimed at workers in artificial intelligence.

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for computer scientists.

Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.

Information is a central topic in computer science, cognitive science and philosophy. In spite of its importance in the 'information age', there is no consensus on what information is, what makes it possible, and what it means for one medium to carry information about another. Drawing on ideas from mathematics, computer science and philosophy, this book addresses the definition and place of information in society. The authors, observing that information flow is possible only within a connected distribution system, provide a mathematically rigorous, philosophically sound foundation for a science of information. They illustrate their theory by applying it to a wide range of phenomena, from file transfer to DNA, from quantum mechanics to speech act theory.

Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Gödel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice, however, there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Gödel's incompleteness theorem and the Church-Rosser theorem. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanisation of metamathematics itself has important implications for automated reasoning since metatheorems can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists and philosophers with some knowledge of logic and computing.

Computational learning theory is a subject which has been advancing rapidly in the last few years. The authors concentrate on the probably approximately correct model of learning, and gradually develop the ideas of efficiency considerations. Finally, applications of the theory to artificial neural networks are considered. Many exercises are included throughout, and the list of references is extensive. This volume is relatively self contained as the necessary background material from logic, probability and complexity theory is included. It will therefore form an introduction to the theory of computational learning, suitable for a broad spectrum of graduate students from theoretical computer science and mathematics.

This book discusses the connection between two areas of semantics, namely the semantics of databases and the semantics of natural language, and links them via a common view of the semantics of time. It is argued that a coherent theory of the semantics of time is an essential ingredient for the success of efforts to incorporate more 'real world' semantics into database models. This idea is a relatively recent concern of database research but it is receiving growing interest. The book begins with a discussion of database querying which motivates the use of the paradigm of Montague Semantics and discusses the details of the intensional logic ILs. This is followed by a description of the author's own model, the Historical Relational Data Model (HRDM) which extends the RDM to include a temporal dimension. Finally the database querying language QEHIII is defined and examples illustrate its use. A formal model for the interpretation of questions is presented in this work which will form the basis for much further research.

Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students and researchers in theoretical computer science.

Action Semantics is a novel approach to the formal description of programming languages. Its abstractness is at an intermediate level, between that of denotational and operational semantics. Action Semantics has considerable pragmatic advantages over all previous approaches, in its comprehensibility and accessibility, and especially in the usefulness of its semantic descriptions of realistic programming languages. In this volume, Dr Peter Mosses gives a thorough introduction to action semantics, and provides substantial illustrations of its use. Graduates of computer science or maths who have an interest in the semantics of programming languages will find Action Semantics a most helpful book.

This book tackles the problems of update algorithms for databases. How can one construct and maintain a database of facts, capable of incorporating new information and getting rid of all outdated information, and yet in the process not disturb any other information in the database? The author has produced a formal method for specifying the desired change intentionally, using a 'formula-based' approach to updating needs rather than a 'model-based' technique. The complexity of the algorithms, choice of semantics and a means of enforcing integrity constraints are also discussed. The book will be of value to all involved in database research.

All traditional implementation techniques for functional languages (mostly based on supercombinators, environments or continuations) fail to avoid useless repetition of work; they are not 'optimal' in their implementation of sharing, often causing a catastrophic, exponential explosion in reduction time. Optimal reduction is an innovative graph reduction technique for functional expressions, introduced by Lamping in 1990, that solves the sharing problem. This book, the first in the subject, is a comprehensive account by two of its leading exponents. Practical implementation aspects are fully covered as are the mathematical underpinnings of the subject. The relationship to the pioneering work of Lévy and to Girard's more recent Geometry of Interaction are explored; optimal reduction is thereby revealed as a prime example of how a beautiful mathematical theory can lead to practical benefit. The book is essentially self-contained, requiring no more than basic familiarity with functional languages. It will be welcomed by graduate students and research workers in lambda calculus, functional programming or linear logic.

Information retrieval, IR, the science of extracting information from any potential source, can be viewed in a number of ways: logical, probabilistic and vector space models are some of the most important. In this book, the author, one of the leading researchers in the area, shows how these views can be reforged in the same framework used to formulate the general principles of quantum mechanics. All the usual quantum-mechanical notions have their IR-theoretic analogues, and the standard results can be applied to address problems in IR, such as pseudo-relevance feedback, relevance feedback and ostensive retrieval. The relation with quantum computing is also examined. To keep the book self-contained appendices with background material on physics and mathematics are included. Each chapter ends with bibliographic remarks that point to further reading. This is an important, ground-breaking book, with much new material, for all those working in IR, AI and natural language processing.

This book is an extended collection of revised contributions that were initially submitted to the International Workshop on Adaptive Multimedia Retrieval (AMR 2005). This workshop was organized during July 28-29, 2005, at the U- versity of Glasgow, UK, as part of an information retrieval research festival and in co-location with the 19th International Joint Conference on Arti?cial Int- ligence (IJCAI 2005). AMR 2005 was the third and so far the biggest event of the series of workshops that started in 2003 with a workshop during the 26th German Conference on Arti?cial Intelligence (KI 2003) and continued in 2004 as part of the 16th European Conference on Arti?cial Intelligence (ECAI 2004). Theworkshopfocussedespeciallyonintelligentmethodstoanalyzeandstr- ture multimedia collections, with particular attention on methods that are able to support the user in the search process, e. g. , by providing additional user-and context-adapted information about the search results as well as the data coll- tion itself and especially by adapting the retrieval tool to the user’s needs and interests. The invited contributions presented in the ?rst section of this book— “Putting the User in the Loop: Visual Resource Discovery” from Stefan Rug ¨ er, “Using Relevance Feedback to Bridge the Semantic Gap” from Ebroul Izquierdo and Divna Djordjevic, and “Leveraging Context for Adaptive Multimedia - trieval: A Matter of Control” from Gary Marchionini—illustrate these core t- ics: user,contextandfeedback. Theseaspectsarediscussedfromdi?erent points ofviewinthe18contributionsthatareclassi?edintosixmainchapters,following rather closely the workshop’s sessions: ranking, systems, spatio-temporal re- tions, using feedback, using context and meta-data.