Birkhoff Completeness in Institutions

Logica Universalis 2 (2):277-309 (2008)
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
Keywords Proof theory  institutional model theory  Horn sentences  Birkhoff completeness  abstract substitutions
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