Turner has gathered the latest results of research on the development of formal languages and formal logics for knowledge representation systems that must reason about modality and truth. Although this book might serve as a textbook for an advanced graduate course in knowledge representation, it is more likely to appear on the shelves of many AI researchers as a good reference on truth theories and modal logic. The compactness of the book and the inclusion of a number of formal proofs make it desirable that readers have some prior knowledge of the use of formal logics (such as predicate calculus and propositional logic) as knowledge representation schemes.

The first chapter serves as a brief introduction to the notion of reasoning agents. That is, any knowledge representation system must be able to both represent and distinguish three different types of assertions: an agent believes a proposition, an agent knows that a proposition is true, and an agent believes a proposition that is actually false. A number of logics (and formal languages) have been espoused for the representation of modalities. The author’s intent, however, is to place bounds on the possible forms of these logics by restricting theories to being first-order (which is, according to the author, “most natural and computationally tractable”). In this light, the author describes propositions from the viewpoints of various paradigms: propositions as possible worlds, propositions as sentences, propositions as primitives, and so on.

The second chapter provides a brief introduction to lambda calculus and predicate calculus, leading up to a formal derivation of the inconsistencies found in the natural axioms for truth as given by the Tarski biconditionals. This chapter sets the theme for the first half of the book, that is, the development of formal logics of truth.

In the third chapter, the author considers a way of avoiding the inconsistencies of classical logic by introducing three-valued logic. The particular three-valued logic presented is based upon Kleene strong three-valued logic. Rather than abandoning classical logic, the author chooses to base the logic of truth itself upon Kleene logic. The first part of the chapter is a brief coverage of Kleene logic. The theory is then reformulated to look more like classical two-valued logic by defining an assertion as being either Kleene-true or Kleene-false.

In the fourth chapter, a particular consequence of three-valued logic, the rejection of the principle that states that every logical truth must be true, is discussed under the heading of stable truth. Logics of stable truth, stable axioms, and necessitation are included in this chapter.

The fifth chapter is the final chapter in the first major theme of the book, the development of formal logics of truth. The last truth theory presented is an extension of lambda calculus by adding logical combinators. This theory is known as the Frege structures theory and is a highly intensional theory that can be used in natural language semantics.

Chapters 6 through 8 represent the second major theme of the book, modality and its interaction with truth. Traditional modal logic is covered in chapter 6. In the seventh chapter, the author develops three truth theories within the context of traditional modal logic. Chapter 8 is a discussion of possible “natural and consistent modal systems of predictable modality.”

Since the intent of the book is to provide an overview of recent research on various logics of truth and modality, no one theory is developed extensively. Instead, a list of additional references is provided at the end of the book. The format of the book is ideal for someone who wishes to begin with an overview of a particular logic, see how it compares with other logics in terms of strengths and shortcomings, and then investigate the logic in greater detail by using the references provided. Those readers with a background in formal logics who are not easily intimidated by formal definitions and proofs should enjoy this book as an addition to their knowledge representation libraries.