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In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true propositions. The series of formulas which is constructed within such a system is called a derivation and the last formula of the series is a theorem, whose derivation may be interpreted as a proof of the truth of the proposition represented by the theorem.
Truthfunctional propositional logic is a propositional logic whose interpretation limits the truth values of its propositions to two, usually true and false. Truthfunctional propositional logic and systems isomorphic to it are considered to be zeroth order logic.
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