Inconsistency of production systems

摘要

Production systems are widely used for knowledge representation in expert systems. Using production systems it is possible to specify inconsistent knowledge, but in the case of inconsistency the world kept in mind when establishing the knowledge is most probably not formalized. Another reason for the relevance of consistency results from a logical point of view because any formula can be derived from an inconsistent theory.Thus, we consider special production systems motivated by the knowledge representation form used in various expert system shells. We define inconsistency for this kind of production systems. Afterwards we give a logical description such that inconsistent production systems are represented by unsatisfiable propositional calculus formulas and vice versa. We present algorithms deciding inconsistency of production systems and analyze their complexity. We also consider problems connected with inconsistency arising when using external databases or allowing user inputs. Finally, we investigate the complexity of production systems with negation proving that these production systems are more expressive than those without negation.Our considerations should be regarded as a step towards an exact formal definition of inconsistency of production systems and its complexity.