Abstract: By embedding the dynamic characteristics into the finite Cantor set X and improving it, a novel mathematics structure and model was obtained,which is P-sets(Packet sets). P-sets is a set pair composed of internal P-set XI' (in- tonal packet set XF)and outer P-set XF (outer packet set XF) , or (XF , XF ) is P-sets. Based on P-sets, internal P-rca-soning(internal packet rcasoning),out p-rcasoning(outer packet reasoning)，Prcasoning(packet reasoning) and the dia-grammatic representation of reasoning model were given. The structure of P-reasoning is "if (ak，。穿.，)今(菇，，潇)，then((二)象1，(二)穿)今((二)奋，(二)象1)”.A few theorems were presented, which are internal P-reasoning and information de-leting theorem, outer P-reasoning and information supplementing theorem, P-reasoning and information deleting-supple-menting theorem, the relation theorem of P-reasoning and general reasoning and so on. A few concepts were given,which arc information unit circle, internal P-reasoning information circle and outer P-reasoning information circle. Thedynamic characteristics theorem of P-reasoning information circle was given. The internal discovery and outer discoverycriterion of reasoning information circlcunknown information were given. By using the results, the application of inter-nal packet reasoning in the unknown internal information discovery-identification was given. The attribute perturbationcharacteristic of P-reasoning,internal P-perturbation theorem of internal P-reasoning, outer P-perturbation theorem of outer P-reasoning and P-perturbation of P-reasoning were obtained using the dynamic characteristic of P-rcasoning.In the internal P-easoning,owing to the existence of internal P-perturbation, part information in the internal P-reasoning conclusion is lost. In the outer P-reasoning, owing to the existence of outer P-perturbation, part information is supple-mented into the outer P-reasoning conclusion. P-sets is a novel model and method with good application prospect in the intelligent information system.

Key words: P-sets, P-reasoning, Information deleting, Information supplementing, Information unit circle, Unknown information discovery, Application