Normal Forms, Proof and Argument

Abstract

In boolean logic, logical formulae are usually reduced to standardised (or normalised) forms, which are more appropriate for automated theorem proving. Such an example are the disjunctive normal form (d.n.f), represented by conjunctive clauses connected by the disjunction operator (OR, $\vee$), and the conjunctive normal form (c.n.f), represented by disjunctive clauses connected by the conjunction operator (AND, $\wedge$). In this Chapter we present the formal definition and derivation of d.n.f and c.n.f, along with some deduction rules. We then present some popular arguments such as the proof by contradiction, the proof by induction and the pigeonhole principle.