All literals implied by a set of horn clauses What is the name of this problem: given a set of Horn clauses (in fact just definite clauses and facts), find the set of literals which can be deduced from it. E.g. given $\{a, a \Rightarrow b, b \wedge c \Rightarrow d\}$, output $\{a, b\}$.
It's called finding a minimal model of a Horn formula.

This model is unique because the intersection of two models of a Horn formula is itself a model. In fact, [Horn, On sentences which are true of direct unions of algebras, 1951] proved the following: A boolean function can be expressed as a conjunction of Horn clauses if and only if its set of models is closed under intersection.