On Abstracting Decision Procedures for Non-monotonic Reasoning

The author has recently introduced a meta-level speciication for non-monotonic theories which has default theories , normal logic programs and separated autoepistemic theories as instances. Semantics including the stable, stationary and regular semantics are generalized for non-monotonic theories satisfying the speciication in a straightforward way. Most importantly, it is possible to prove properties of semantics directly from the speciication and independently of the instances. This paper provides a preliminary discussion of extending the speciication to cover computational issues of the instances. It is expected that properties such as decidability and computational time complexity can be addressed by distinguishing non-monotonic theories that are nitely character-izable. Moreover, it seems that meta-level decision procedures can be devised to cover reasoning corresponding to any nitely characterizable non-monotonic theory.