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Propositional Logic Semantics
Recall homework01.
Let .
Interpretation for propositional logic is a function .
We next define evaluation function: \[
e : F \to (I \to {\cal B})
\]
by recursion on formula syntax tree:
This definition follows one in the formula evaluator in homework01.
We denote by \[
I \models F
\] and denote by \[
I \not\models F
\]
Validity and Satisfiability
Formula is valid iff . We write this simply \[
\models F
\]
Formula is satisfiable iff
Formula is contradictory iff