Logics for Artificial Intelligence

Abstract

Turner leads us on a whirlwind tour of nonstandard logics and their general applications to Al and computer science.Many Al problems resist straightforward translation into classical logic. Reasoning with uncertain or incomplete information, modeling temporal relationships, and formalizing knowledge and belief models-three issues important to Al-are difficult to satisfactorily represent in standard logic. In the quest for adequate formal models of these and other Al problems, researchers are exploring alternative, nonstandard logics.Turner divides nonstandard logics into two categories-those extending classical logic and those rivaling it. Extensions achieve greater expressive power through a richer operator vocabulary; for example, the modal logic operators M and L for logical possibility and logical necessity. Rival logics reject some classical-logic theorems such as the law of the excluded middle (probably not provable in fuzzy or threevalued logic).In dealing with extensions, Turner discusses modal and temporal logic. He covers the following rival systems: multiple-valued logic, intuitionist logic, nonmonotonic inference, and fuzzy logic. For each system, he presents the rationale and fundamental tenets common to all variants, and then critically reviews the most important variants of each logic. Some chapters include extended examples of applying nonstandard logic to research problems in computer science.Turner seeks to convey the state of the art in each area, and to provide pointers into the literature for background information and further study. To cover six kinds of logic in 120 pages, exposition must be brisk. Although the book is self contained and the author clearly separates important points from details, readers should have firm foundations in classical logic plus healthy appetites for formalism. The chapters on modal, temporal, and intuitionist logic exemplify promising applications of nonstandard logics to active computer science research. Modal logic is used to develop formal semantic specification for a simple programming language.The sample application of intuitionist logic shows how logic can be used simultaneously as a specification and a programming language, making possible program specifications directly executable as code. Temporal logic is applied to problems involving specification and verification of digital hardware components. These sample applications reveal to nonlogicians the rewards for investing time and effort to learn yet another logi-cal variety. One only wishes Turner had given illustrative applications for every logical system surveyed.On the negative side, the book's most annoying faults are excessive typographical errors (literally hundreds) and mangled bibliographical entries. The title's reference to Al is misleading as well. Although some logical systems discussed have special relevance to Al (nonmonotonic and fuzzy logic, for example), others relate to theoretical computer science in general but not to Al in particular. At times, the author presupposes more backgroun...

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