Birkhoff Completeness in Institutions

Abstract.We develop an abstract proof calculus for logics whose sentences are ‘Horn sentences’ of the form: $$(\forall X)H \Rightarrow c$$ and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the ‘Horn fragment’ of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.

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