A DPLL Proof Procedure for Propositional Iterated Schemata

We investigate iterated schemata whose syntax integrates arithmetic parameters, indexed propositional variables (e.g. Pi), and iterated conjunctions/disjunctions (e.g. Vn i=1 Pi, where n is a parameter). Using this formalism gives us some extra information about the structure of the problem, which can be used in order to prove such a schema for all values of the parameters. The structure of the formula is used as a guide for the structure of the proof. We define a Davis-Putnam-LogemannLoveland based procedure for iterated schemata that we show to be sound and complete (w.r.t. satisfiability). Though unrestricted schemata are incomplete (w.r.t. provability) we show, by extending our procedure, that cycles can be detected in the proof tree, thus allowing to prove some schemata that are neither provable nor refutable in the initial calculus. An example shows how this method allows to tackle non-trivial problems. We give evidence that our procedure is a useful tool for identifying complete classes of schemata.