Satisfiabilité

Anglais

Satisfiability

In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true.[1] A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false. These four concepts are related to each other in a manner exactly analogous to Aristotle's square of opposition.

The four concepts can be raised to apply to whole theories: a theory is satisfiable (valid) if one (all) of the interpretations make(s) each of the axioms of the theory true, and a theory is unsatisfiable (invalid) if all (one) of the interpretations make(s) each of the axioms of the theory false.

It is also possible to consider only interpretations that make all of the axioms of a second theory true. This generalization is commonly called satisfiability modulo theories.