Single Idea 10752

[catalogued under 5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-]

Full Idea

Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'.

Gist of Idea

Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true

Source

Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2)


A Reaction

We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another.