Propositional logic
Propositional logic or sentential logic is the logic of propositions, sentences, or clauses. Unlike predicate logic or syllogistic logic, the internal structure of a clause or sentence has no effect on validity in propositional logic. Instead, validity is determined by the relationship of the clauses to each other in sentences compounded with words like 'and', 'or', and 'if ... then ...'. So the smallest possible expressions in a propositional logic (its atomic formulas) are clauses or variables that stand for clauses. Such variables are called propositional variables.
In general terms, a propositional or sentential calculus is a formal system that consists of a set of syntactic expressions (well-formed formulae, formulas, or wffs), a distinguished subset of these expressions, plus a set of transformation rules that define a binary relation on the space of expressions. Most systems of propositional logic also have a formal semantics that specifies how the truth or falsity of a compound sentence is determined by the truth values of its clauses and connecting words.
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