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 to represent propositions. A system of inference rules and axioms allows certain formulas to be derived. These derived formulas are called theorems and may be interpreted to be true propositions. Such a constructed sequence of formulas is known as a derivation or proof and the last formula of the sequence is the theorem. The derivation may be interpreted as proof of the proposition represented by the theorem.
Usually in Truth-functional propositional logic, formulas are interpreted as having either a truth value of true or a truth value of false.[clarification needed] Truth-functional propositional logic and systems isomorphic to it, are considered to be zeroth-order logic.
Contents
- 1 History
- 2 Terminology
- 3 Basic concepts
- 4 Generic description of a propositional calculus
- 5 Example 1. Simple axiom system
- 6 Example 2. Natural deduction system
- 7 Basic and derived argument forms
- 8 Proofs in propositional calculus
- 9 Soundness and completeness of the rules
- 10 Interpretation of a truth-functional propositional calculus
- 11 Alternative calculus
- 12 Equivalence to equational logics
- 13 Graphical calculi
- 14 Other logical calculi
- 15 Solvers
- 16 See also
- 17 References
- 18 Further reading
- 19 External links
