Sometimes formulations appear below with the phrase "(generalized) consequence relation", meaning that the claim being made or considered applies both in the case of consequence relations and in the case of generalized consequence relations.
As the ∨ example makes clear, by contrast with the case of consequence relations, Val, for a generalized consequence relation ⊩, need not be closed under conjunctive combinations.[7] Again, one can see this in the light of the considerations of Section 1, thinking of the relational connection between Set-Set sequents and arbitrary valuations, with the relation being 'holds on'.
Sounds like an obvious case of consequences, but as with most research, this paper carefully notes a link, not necessarily a cause.
How should we understand cases of logical consequence from infinitely many premises?
One of the more curious cases of unintended consequences begins with the 1993 tax law.
The reduction in the number of requests for consultations during the second year can also be interpreted as a better selection of cases, a consequence of an improvement in specialist activity.
"I have a duty to fulfill as attorney general, and the immediate need to focus on a case of great consequence.
"I have a duty to fulfill as attorney general — and the immediate need to focus on a case of great consequence.
In the case of Scott consequence relations, Γ ⊨ Δ means that the joint truth of all the members of Γ implies (in some sense) the truth of at least one member of Δ.
But in its own perhaps less flashy way this term might well measure up to the last one for cases of far-reaching consequence.
