Reasoning on schemata of formulæ

Authors:
Mnacho Echenim;Nicolas Peltier
Affiliations:
LIG, Grenoble INP/CNRS, University of Grenoble, France;LIG, Grenoble INP/CNRS, University of Grenoble, France
Venue:
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Year:
2012

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Abstract

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.