In this chapter, we introduce the propositional and the predicate calculi as representation languages for artificial intelligence. The importance of logic and the predicate calculus was discussed in ► Sect. 1.6 ; its advantages include a well-defined formal semantics and sound and complete reasoning rules. This chapter begins, ► Sect. 7.1, with a brief review of the propositional calculus. ► Section 7.2 describes the syntax and semantics of the predicate calculus.