ITL
© 1996-2018







II.6 Semantics of Propositional Logic

Semantics [Slide 38]

Let M() be the “meaning” function from Propositions × State to {tt,} and let σ0 be a state then

Mtrue(σ0)
tt
MP(σ0)
σ0(P)
M¬f(σ0)
not (Mf(σ 0))
Mf1 f2(σ0)
(Mf1(σ0) and Mf2(σ0))

Semantics [Slide 39]

Example 5.

Let σ0(P) = tt and σ0(Q) = .

MP Q(σ0)
=
M¬(¬P ¬Q)(σ0)
=
not (M¬P ¬Q(σ0))
=
not (M¬P(σ0) and M¬Q(σ0))
=
not (not (MP(σ0)) and not (MQ(σ0)))
=
not (not (σ 0(P)) and not (σ0(Q)))
=
not (not (tt) and not ())
=
not ( and tt)
=
not ()
=
tt







2018-03-10
Contact | Home | ITL home | Course | Proofs | Algebra | FL