Syntax Propositional Logic

II.2 Syntax Propositional Logic

Propositional Logic [Slide 21]

Summary of the syntax of Propositional Logic:

Boolean values: true,false
Boolean variables: P,Q,…
meta-variables: f,f₁,f₂,…
Boolean operators:

∧

(And),

∨

(Or),

¬
(Not),

⊃

(Implication),

≡

(Equivalence)

Propositional Logic [Slide 22]

Syntax of propositional formulae in BNF (grammar):

f ::=

true | P |¬f | f₁ ∧ f₂

Derived Boolean operators:

false	≜	¬true
f₁ ∨ f₂	≜	¬(¬f₁ ∧¬f₂)
f₁ ⊃ f₂	≜	¬f₁ ∨ f₂
f₁ ≡ f₂	≜	(f₁ ⊃ f₂) ∧ (f₂ ⊃ f₁)

2023-09-12

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