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where <math>A,B_{1},\dots,B_{m},C_{1},\dots,C_{n}</math> are ground atoms. If {{mvar|P}} does not contain negation (<math>n=0</math> in every rule of the program) then, by definition, the only stable model of {{mvar|P}} is its model that is minimal relative to set inclusion.<ref>This approach to the semantics of logic programs without negation is due to Maarten van Emden and [[Robert Kowalski]] [1976].</ref> (Any program without negation has exactly one minimal model.) To extend this definition to the case of programs with negation, we need the auxiliary concept of the reduct, defined as follows.
For any set {{mvar|I}} of ground atoms, the ''reduct'' of {{mvar|P}} relative to {{mvar|I}} is the set of rules without negation obtained from {{mvar|P}} by first dropping every rule such that at least one of the atoms {{
:<math>B_{1},\dots,B_{m},\operatorname{not} C_{1},\dots,\operatorname{not} C_{n}</math>
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