Hyperresolution for guarded formulae

Authors:
Lilia Georgieva;Ullrich Hustadt;Renate A. Schmidt
Affiliations:
Department of Computer Science, University of Manchester, Oxford Road, Manchester M13 9PL, UK;Department of Computer Science, University of Liverpool, Liverpool L69 7ZF, UK;Department of Computer Science, University of Manchester, Oxford Road, Manchester M13 9PL, UK
Venue:
Journal of Symbolic Computation - Special issue: First order theorem proving
Year:
2003

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Abstract

This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general, hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments of the guarded fragment which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1- and point out several ways of extending this fragment without losing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution.