# Propositional Logic Semantics

Recall homework01.

Let .

**Interpretation** for propositional logic is a function .

We next define evaluation function:

by recursion on formula syntax tree:

This definition follows one in the formula evaluator in homework01.

We denote by

and denote by

## Validity and Satisfiability

Formula is valid iff . We write this simply

Formula is satisfiable iff

Formula is contradictory iff