PARTS INFERENCE: Closed and Semi-Closed Partitioning Graphs

Ma consider the problem of answering pa r t o f quest ions and quest ions about over lap in p a r t i t i o n i n g s t r u c t u r e s . which is of importance in A . I . systems knowledgeable about pa r t s r e l a t i o n s h i p s , set i nc lus ion r e l a t i o n s h i p s or taxonomies of types in an e a r l i e r paper 1t was noted that the problem of e x t r a c t i n g informat ion from a r b i t r a r y sets o f p a r t i t i o n i n g asser t ions ( "P-graphs") Is i n t r a c t a b l e (at least if P = NP) and the more r e s t r i c t i v e c lass of quas i h i e ra r ch i ca l c losed P-graphs was introduced as a f a i r l y f l e x i b l e rep resen ta t i on o f p a r t i t i o n i n g s t ruc tu res p e r m i t t i n g e f f i c i e n t in fo rmat ion e x t r a c t i o n . The present paper int roduces the larger c lass of semi-closed P-graphs. and prov ides e f f i c i e n t and complete methods fo r answering p a r t o f and d i s j o i n t n e s s quest ions based on such P-graphs