Interpretation

An interpretation or valuation $v$ is a function that assigns a truth-value to every propositional symbol $P$, hence $v(P) \in \{ 0, 1 \}$.

• If $v(P)=1$, then $P$ is true under the interpretation $v$.
• If $v(P)=0$, then $P$ is false under the interpretation $v$. An interpretation is extended to all well-formed formula using truth-tables.

As oppossed to FC1, we include an extra column for for interpretation. For example, take $p\wedge q$, we generate the following truth table:

interpretation	$p$	$q$	$p\wedge q$
$v_0$	F	F	F
$v_1$	F	T	F
$v_2$	T	F	F
$v_3$	T	T	T