Abstract: P-scts(Packct sets) is a set pair (XF，XF) composed of internal P-set XF (internal packet set XF)and outer Pset XI' (outer packet set XI' ) , or (XI' , XI' ) is P-sets. P-sets has dynamic characteristics(XI' has internal dynamic characteristic and了has outer dynamic characteristic). P-sets has been applied in many fields of dynamic information systans. There is a class of information system which has internal dynamic characteristic but has not outer dynamic characteristic. To study the class of information system, Half P-sets(half packet sets) was proposed by improving and simpliEying P-sets in this paper. Half P-sets is a set pair composed of internal P-set XF and finite general set X, or (XF , X) is Half P-sets. Half P-sets has internal dynamic characteristic. hhis paper gave the relation between Half P-sets and finite general set, the relation between Half P-sets and P-sets. By using Half P-sets, the concepts on information internal-truth degree and information internal-truth degree ring were given. Moreover,the information internal-truth degree ring theorems, the criterion of internal-truth degree and the criterion characteristic coefficient about internal-information recovery-reduction. Finally, the application of internal-truth degree ring about internal-information recovery-reduction was provided by employing these results. Half P-sets is a new mathematical method and mathematical model for researching the class of dynamic information system. Half P-sets has good application foreground in the class of dynamic information system.

Key words: Half P-sets, Information internal-truth degree, Information internal-truth degree ring, Internal-truth degreering thcorcm, Information discovery, Application