Theory Resolution: Building in Nonequational Theories

Mark E. Stickel

Theory resolution constitutes a set of complete proce-dures for building nonequational theories into a resolution theorem-proving program so that axioms of the theory need never be resolved upon. Total theory resolution uses a deci- sion procedure that is capable of determining inconsistency of any set of clauses using predicates in the theory. Partial theory resolution employs a weaker decision procedure that can determine potential inconsistency of a pair of literals. Applications include the building in of both mathematical and special decision procedures, such as for the taxonomic information furnished by a knowledge representation sys-tem.

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