A simple but powerful system of logic for representing implications between logically compound sentences, such as `either A or not B', `if B then A', etc. The system will prove, for example, that each of these two sentences implies the other. See also Predicate Calculus/Predicate Logic, Rules of Inference.
In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows to establish that certain formulas are "theorems" of the formal system.