Set Theory for Computing: From Decision Procedures to Declarative Programming with Sets

ISBN-13: 9780387951973 / Angielski / Twarda / 2001 / 409 str.

Domenico Cantone; Eugenio Omodeo; Alberto Policriti

Opis

"Set Theory for Computing" provides a comprehensive account of set-oriented symbolic manipulation methods suitable for automated reasoning. Its main objective is twofold: 1) to provide a flexible formalization for a variety of set languages, and 2) to clarify the semantics of set constructs firmly established in modern specification languages and in the programming practice. Topics include: semantic unification, decision algorithms, modal logics, declarative programming, tableau-based proof techniques, and theory-based theorem proving. The style of presentation is self-contained, rigorous and accurate. Some familiarity with symbolic logic is helpful but not a requirement. This book is a useful resource for all advanced students, professionals, and researchers in computing sciences, artificial intelligence, automated reasoning, logic, and computational mathematics. It will serve to complement their intuitive understanding of set concepts with the ability to master them by symbolic and logically based algorithmic methods and deductive techniques.

Recenzje

From the reviews:

"The book is an up-to-date and well-organized collection of techniques and results concerning the problem of dealing with sets in computer science. ... In particular, the book can be very interesting for postgraduate students and researchers in computer science and logic. ... The book is largely self-contained and the style of presentation is extremely rigorous and accurate. ... this will become a sort of classic work for automated deduction and declarative programming and surely it deserves to find a place in all scientific libraries." (A. Dovier, Theory and Practise of Logic Programming, Vol. 3 (1), 2003)

"Set theory has played the role of a lingua franca for modern mathematics. The authors of this monograph intend to extend this service to computer science, artificial intelligence, and computational mathematics. ... Several variants of ZF, which are meant for different applications, are surveyed and concrete, computable models are investigated. ... There is an extensive list of references, an index of symbols and an index of terms." (J.M. Plotkin, Zentralblatt MATH, Vol. 981, 2002)

Spis treści

What is Computable Set Theory? * Logical Background * Axiomatic Views of Aggregates * Semantic Views of Aggregates * Sets for Problem Solving * Decision Problems and Some Solutions * Inference Techniques and Methods * Set/Hyperset Unification Algorithms * A Syllogistic Solitaire * Stratified Syllogistics * Quantitative Set Reasoning * Set Theory for Non-Classical Logics * Logic Programming With Sets * Syllogistic Tableaux