Reasoning on Schemata of Formulæ

Mnacho Echenim (1) , Nicolas Peltier (1)

1 CAPP - Calculs algorithmes programmes et preuves

A logic is presented for reasoning on iterated sequences of formulæ over some given base language. The considered sequences, or schemata, are defined inductively, on some algebraic structure (for instance the natural numbers, the lists, the trees etc.). A proof procedure is proposed to relate the satisfiability problem for schemata to that of finite disjunctions of base formulæ. It is shown that this procedure is sound, complete and terminating, hence the basic computational properties of the base language can be carried over to schemata.

Domaines: Logique en informatique [cs.LO]

Mnacho Echenim, Nicolas Peltier. Reasoning on Schemata of Formulæ. AISC 2012 - Artificial Intelligence and Symbolic Computation (Part of CICM 2012), Jul 2012, Bremen, Germany. pp.310-325, ⟨10.1007/978-3-642-31374-5_21⟩. ⟨hal-00933516⟩