Consistent term mappings, term partitions, and inverse resolution
We formalize the notion of inverse substitution, used in the context of inverse resolution, by means of consistent term mappings. An inverse substitution from a clause to a more general clause can also be characterized by means of a term partition. We can generate clauses more general than a given clause by taking an admissible subset of its term occurrences, and constructing a term partition of this subset. We show that these term partitions can be partially ordered. This ordering coincides with the generality of the induced clauses. Similar partitions have been used by Muggleton and Buntine for describing their absorption operator. We show that their absorption algorithm is incomplete, and we give an alternative, complete algorithm, based on our definitions of admissible subset and term partition. We show that under certain conditions, clauses generated by absorption are incomparable with respect to generality. Finally, we relate this to a recent result about least general absorption obtained by Muggleton.
KeywordsInverse resolution absorption substitution
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