Abstract: Inverse P-sets(inverse packet sets) is a new mathematical structure based on P-sets(packet sets). It is a pair of sets composed of internal inverse P-set XF (internal inverse packet set XF) and outer inverse P-set XF (outer inverse packet set)，i. e.is inverse P-sets. Inverse P-sets has dynamic characteristics,the dynamic characteristics of inverse P-sets is identical to that of one kind of information systems. P-sets is obtained by introducing dynamic characteristic into ordinary set X, P-sets has dynamic characteristic, the dynamic characteristics of P-sets is identical to that of another kind of information systems. P-sets has been widely applied to this kind information systems. P-reasoning(packet reasoning) is a reasoning model generated by P-sets, and has dynamic characteristics. On basis of inverse P-sets and inverse P-reasoning,theorem of inverse P-reasoning and internal-outer search was given. The geometric characteristics of inverse P-reasoning was given. Several theorems and applications about inverse P-reasoning and unknown information search-identification were given. Inverse P-sets and inverse P-reasoning have extensive property in practical application.

Key words: Inverse P-sets,Inverse P-reasoning,Search theorem,Geometric characteristic,Application