A Classification of Non-liftable Orders for Resolution
نویسنده
چکیده
In this paper we study the completeness of resolution when it is restricted by a non-liftable order and by weak subsumption. A non-liftable order is an order that does not satisfy A ≺ B ⇒ AΘ ≺ BΘ. Clause c1 weakly subsumes c2 if c1Θ ⊆ c2, and Θ is a renaming substitution. We show that it is natural to distinguish 2 types of non-liftable orders and 3 types of weak subsumption, which correspond naturally to the 2 types of nonliftable orders. Unfortunately all natural combinations are not complete. The problem of the completeness of resolution with non-liftable orders was left open in ([Nivelle96]). We will also give some good news: Every non-liftable order is complete for clauses of length 2, and can be combined with weak subsumption.
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