Appendix A

Review of Classical Logic

Logic, n: The art of thinking and reasoning in strict accordance with the limitations and incapacities of human misunderstanding.

—Ambrose Bierce

A.1 Introduction

A.1.1 What is Logic?

The study of logic can be seen from two viewpoints. The first is where logical systems are seen as being self-contained and not meant to model any real-world objects or actions. Philosophers and logicians have typically studied such systems, developing and extending various different notions of truth, provability etc.

An alternative view of logic, and one that we tend to follow, is as a formalization of some aspect of the real world. Here, a logical system describes, or models, some abstraction of objects or actions that either do, or may, occur in real life. But logic is not the only language that can be used to describe such aspects. For example, English is a language that has been widely used to describe and reason about situations and problems. However, to discover the validity or consistency of a statement in English, the ambiguities and inconsistencies of natural language must be overcome; lawyers often make a living from arguing about the meaning of statements in English!

Thus, a more ‘formal’ language with well-defined semantics and a consistent reasoning mechanism is required; logical systems fit into this category. However, if logic is used to model properties of the real world, we must recognize that a logic represents a particular abstraction. Naturally, ...

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