Propositional model:
Hence a propositional model was simply an assignments of truth values to propositions. In distinguish, a first-order model is a pair (Δ, Θ) where
- Δ is a domain and a non-empty set of 'objects' that is things in which our first-order sentences are refering to.
- Θ is an interpretation or a procedure for calculating the truth of sentences relative to Δ.
Thus it seems very different from propositional logic. Opportunely, everything we have discussed is much far about deduction carries over in first-order logic where we use this new definition of model.