ITL
© 1996-2015







5 Semantics of Propositional Logic

Let ⟦...⟧ be the “meaning” function from Propositions × State to {tt,ff} and let σ0  be a state then

|----------------------------------|
|⟦true⟧σ0     =^  tt                 |
|⟦p⟧σ0       =^  σ0(p)             |
|⟦f ⟧σ0      =^  not(⟦f ⟧σ0)         |
|⟦f1 ∧ f2⟧σ0  =^  (⟦f1 ⟧σ0 and ⟦f2⟧σ0)  |
------------------------------------

Example 3 Let σ0(p) = tt  and σ0(q) = ff  .

   ⟦p ∨ q⟧σ0
=  ⟦ (p ∧ q)⟧σ0
=  not(⟦p ∧ q ⟧σ0)
=  not(⟦p ⟧σ0 and⟦q⟧σ0)
=  not(not(⟦p⟧σ0)andnot(⟦q⟧σ0))
=  not(not(σ0(p))and not(σ0(q)))
=  not(not(tt)and not(ff ))
=  not(ff andtt)
=  not(ff)
=  tt

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