Initial Limit Datalog: a New Extensible Class of Decidable Constrained Horn Clauses

We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types) of the first-order language limit DatalogZ (a fragment of Datalog modulo linear integer arithmetic), but can be instantiated with any suitable background theory....