Propositional Logic Semantics

Let ${\cal B} = \{{\it true}, {\it false}\}$ .

Interpretation for propositional logic is a function $I : V \to {\cal B}$ .

We next define evaluation function:

$\begin{equation*} e : F \to (I \to {\cal B}) \end{equation*}$

This definition follows one in the formula evaluator in homework01.

We denote $e(F)(I) = {\it true}$ by

$\begin{equation*} I \models F \end{equation*}$

and denote $e(F)(I) = {\it false}$ by

$\begin{equation*} I \not\models F \end{equation*}$

Validity and Satisfiability

Formula is valid iff $\forall I. I \models F$ . We write this simply

$\begin{equation*} \models F \end{equation*}$

Formula is satisfiable iff $\exists I. I \models F$

Formula is contradictory iff $\forall I. I \not\models F$