Definition:Contingent Statement

Definition
A contingent statement is a statement form which is neither a tautology nor a contradiction, but whose truth value depends upon the truth value of its component substatements.

Logical Formula
In the context of logical formulas the term satisfiable is usually used:

A logical formula $$P$$ is satisfiable if its value is True in at least one boolean interpretation.

A logical formula $$P$$ is not-valid or falsifiable if its value is False in at least one boolean interpretation.

Set of Logical Formulas
Let $$U = \left\{{P_1, P_2, \ldots, P_n}\right\}$$ be a set of logical formulas.

Let $$U' = \left\{{p_1, p_2, \ldots, p_m}\right\}$$ be the set of all the atoms of all the logical formulas in $$U$$.

(Some of these atoms, and indeed this will most likely be the case, may be in more than one logical formula.)

Then $$U$$ is (mutually) satisfiable if there exists a boolean interpretation $$v$$ for all the atoms in $$U'$$ such that $$v \left({P_1}\right) = v \left({P_2}\right) = \cdots = v \left({P_n}\right) = T$$.

Also see

 * Tautology
 * Contradiction