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. 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.