Formal (denotational) semantics of Propositional Logic:
Propositions ×State ↦ Bool
proposition: P ∧ (P ∨ Q)
state σ: semantic value of P is tt and of Q is ff
P | Q | (P ∨ Q) | P ∧ (P ∨ Q) |
tt | ff | tt | tt |
A state is a mapping State from the set of propositional variables Varb to the set of Boolean values Bool ≜{tt,ff}.
State : Varb ↦ Bool
We will use σ0,σ1,σ2,… to denote states and Σ to denote the set of all possible states.