Review of The logic of knowledge bases.

Abstract

HECTOR J. LEVESQUE AND GERHARD LAKEMAYER The Logic of Knowledge Bases Cambridge, MA: The MIT Press, 2000, 300 pages (ISBN 0-262-122324, us$45, Hardcover) Reviewed by MICHAEL R. W. DAWSON Many researchers (e.g., Dawson, 1998; Marr, 1982; Pylyshyn, 1984) have argued that a complete account of cognition requires that three qualitatively different questions be answered: information processing problem is being algorithm is being used to solve the problem? physical mechanisms are responsible for implementing this algorithm? Cognitive science is interesting, difficult, and interdisciplinary because answering each of these questions requires dramatically different methods. For this reason, it is important for experimental cognitive psychologists to cast their gaze towards other disciplines in order to gain some perspective on how radically different methodologies might provide new insights on cognition. For example, when addressing the question What information processing problem is being solved? cognitive scientists are concerned with the computational level of analysis. At this level, formal methods such as mathematics or logic are used to discover general regularities about cognition that might later lead to experimental investigations that are more typically the province of cognitive psychology. One interesting example of a computational analysis is provided by computer scientists Hector Levesque and Gerhard Lakemeyer in the book under review. Levesque and Lakemeyer begin with a brief overview of the central place that knowledge and knowledge representation hold in artificial intelligence research. They establish themselves firmly in the camp of what Haugeland (1985) would call good old-fashioned by expressing their interest in the study of systems that exhibit intelligence because they manipulate symbolic representations of knowledge. The authors use their book to show how logic can be used to study different aspects of such a system: the way in which information might be stored in it, the language that can be used to interact with it, and the abstract characterization of the relationship between the symbols in a knowledge base and the knowledge of the world for which these symbols stand. The book describes research that is located exclusively at the computational level of analysis, in that it explores knowledge base regularities that do not depend on any specific commitments about what particular information is stored, or about particular algorithms or programming languages used to manage the knowledge base. In the early chapters of their book, Levesque and Lakemeyer define the properties of two different logical languages. The first is a first-order predicate logic that has mostly standard properties, with the exception that it includes some special representational features (standard names and a special treatment of equality) that become important in later proofs. The second is a modal logic designed to represent epistemic states in which the logic can distinguish between predicates that are true and predicates that are known. The first-order predicate logic is a subset of the modal logic; the modal logic also includes the extra logical symbol x So, in the modal logic one could represent an objective fact about the world, such as Tom teaches Sam, with the expression Teach(tom, sam); one could represent knowing this fact with the expression K Teach(tom, sam). When defining the properties of a logic, it is necessary to specify both a syntax and a semantics (e.g., Genesereth & Nilsson, 1987). The authors take a fairly standard approach to syntax, but opt for an interesting position when defining the semantics of their epistemic logic. Usually, one adopts one of two semantics for a modal logic: either a sentential semantics, in which an agent is said to believe something if a logical statement is part of (or can be derived from) a set of logical expressions, or a possible-worlds semantics, in which an agent is associated with a set of possible worlds, and is said to believe an expression if that expression is true in each of these accessible possible worlds. …