Some definitions

There are some definitions applying to rule-based systems which give a base for the theory [13].

• Redundant rules -- There are two basic possibilities of defining redundant rules:
  • a rule is redundant if there exists another rule with identical (up to variables renaming) precondition and conclusion,
  • a rule is redundant if it succeeds in the same situation as another rule and both the rules have the same conclusions.

• Subsumption of rules -- We consider here the most general case of subsumption. A rule subsumes another rule if the following conditions hold:
  • the precondition part of the first rule is weaker (more general) than the precondition of the subsumed rule,
  • the conclusion part of the first rule is stronger (less general) than the conclusion of the subsumed rule.

• Reduction of rules -- The main idea of reduction of rules is to minimize the number of rules without influencing the potential capabilities of the system for inferring new knowledge.

• Completeness of rule-based systems -- A rule-based system is complete if there exists at least one rule succeeding for any possible input situation.