Introduction to Logic and Propositions

Notes

In this chapter, we introduce the study of logic from a mathematical point of view. Mathematical logic finds applications in many areas of computing. The laws of logic are employed in the design of digital circuitry in a computer. Logical expressions occur as conditions in control structures in algorithms and computer programs, and in commands used for querying databases. Expert systems employing knowledge-based software use rules of logical inference to draw conclusions from known facts. Formal specification documents, which state in a precise way what computer systems are required to do, are written in specification languages such as Z, which use the theory and notation of symbolic logic. We begin this chapter by looking at examples involving everyday English sentences. This is followed by an introduction to the more formal mathematical approach used in propositional and predicate logic. The fundamental objects we work with in arithmetic are numbers. Similarly, the fundamental objects in logic are propositions. *Definition:* A proposition is a statement that is either true or false. Whichever of these (true or false) is the case is called the truth value of the proposition. Here ...