From Wikipedia, the free encyclopedia Jump to: navigation,
search  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 tha