Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT, " "OR, " "AND, " and "implies." Many systems of propositional calculus have been devised which attempt to achieve consistency, completeness, and independence of axioms. The term "sentential calculus" is sometimes used as a synonym for propositional calculus. Axioms (or their schemata) and rules of inference define a proof theory, and various equivalent proof theories of propositional calculus can be devised. The following list of axiom schemata of propositional calculus is from Kleene.
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