A formula q5 of L ( =-RRB- , the language with equality , is weakly R + M-abductible from an object theory T , denoted by T I-R + m 0 , iff there exists a partial theory T e PT ( T ) and a preferred model M E PM ( T ) such that M = 0 , i.e. 0 is true in at least one preferred model of the partial theory T. Note : The notions of strong provability and strong R + M-abduction can be introduced by replacing `` there exists '' by `` all '' in the above definitions ( cfXXX Zadrozny 1987b ) .
intended models circumscription and commonsense reasoningquot
W Zadrozny
The set of all preferred models of T is denoted by PM ( T ) . A formula q5 of L ( =-RRB- , the language with equality , is weakly R + M-abductible from an object theory T , denoted by T I-R + m 0 , iff there exists a partial theory T e PT ( T ) and a preferred model M E PM ( T ) such that M = 0 , i.e. 0 is true in at least one preferred model of the partial theory T. Note : The notions of strong provability and strong R + M-abduction can be introduced by replacing `` there exists '' by `` all '' in the above definitions ( cfXXX Zadrozny 1987b ) . We will have , however , no need for `` strong '' notions in this paper .
A formula q5 of L ( =-RRB- , the language with equality , is weakly R + M-abductible from an object theory T , denoted by T I-R + m 0 , iff there exists a partial theory T e PT ( T ) and a preferred model M E PM ( T ) such that M = 0 , i.e. 0 is true in at least one preferred model of the partial theory T. Note : The notions of strong provability and strong R + M-abduction can be introduced by replacing `` there exists '' by `` all '' in the above definitions ( cfXXX @@CITATIONb ) .