Basic Formal Definitions and Methods

Abstract

Chapter 22, Basic Formal Definitions and Methods, deals with formal aspects mentioned earlier in the book. They are logic and truth, information content, and utility. The purpose of these topics is as follows: (a) Is the provided information correct? (b) How much information is provided? (c) Is the information useful? In this chapter we provide the formalisms for these views. It contains mixed formalisms, the first type of formalism deals with knowledge representation. As a prominent example of knowledge representation, classical logic is discussed. We introduce syntax, semantics and reasoning methods in an axiomatic way. As a special case we also discuss the relation to attribute-value representations. In order to deal with incomplete representations, we introduce information theory for guiding the search for missing knowledge. Besides that, the aspect of utility is formally introduced for dealing with optimality questions. For this, a basic terminology about partial orderings is presented. As an addition chapter, it is not required for understanding the previous parts. It is intended as a support for this book’s readers. It discusses formal aspects in the adopted terminology, which is often varying in the literature. It does not include a tools section.