lectures.alex.balgavy.eu

Lecture notes from university.
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      1 +++
      2 title = 'Semantic entailment'
      3 +++
      4 # Semantic entailment
      5 ϕ₁, …, ϕn ⊨  Ψ
      6 
      7 A formula Ψ is semantically entailed by premises (ϕ₁, …, ϕn) if every valuation that makes premises true makes Ψ true.
      8 
      9 counterexample makes premises true but not conclusion
     10 
     11 if ϕ ⊨ Ψ and Ψ ⊨ ϕ, ϕ ≡ Ψ
     12 
     13 ![Semantic entailment](11bb7fc4feb2fffc9faa39267a68a701.png)
     14 ![Semantic equivalence](b0e73f3474b3ae38b7ea5452e14d53e3.png)