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Preserving Consistency Across Abstraction Mappings

An abstraction mapping over clausal form theories in first-order predicate calculus is presented that involves the renaming of predicate symbols. This renaming is not 1-1, in the sense that several predicate symbols Ri,..., Rn from the original theory are all replaced by a single symbol R in the abstract theory. In order to preserve consistency, however, the clauses that distinguish the Ri's must be discarded in the abstract theory. This leads to a simple semantics; the union of the extensions of each of the Ri's in any model of the original theory forms the extension of R in a model of the abstract theory.