Interpretation in Propositional Logic

An interpretation of a propositional logic formula is an assignment of a value (true or false) to each atom. There are 2ⁿ possible interpretations of a formula with n atoms. Although this is large, it is finite; thus, every question about propositional logic is decidable.

Terminology:

• A formula is valid if it is true under every possible interpretation: P ∨ ¬ P. Otherwise, it is invalid: P.
• A formula is consistent or satisfiable if it is true under some interpretation. If it is false under every interpretation, it is inconsistent or unsatisfiable: P ∧ ¬ P.

If a formula F is true under an interpretation I, I is a model for F.

Two formulas F and G are equivalent if they have the same values under every interpretation: F ↔ G .