Probability, logic \ learning synthesis: formalizing prediction concept

S. O. Smerdov ; E. E. Vityaev

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 340-365

Résumé

Presented paper is devoted to the question of prediction formalized in probabilistic and logical terms. The aim of investigation is to examine different methods such as based on SLD-inferences and alternative semantic approach. Prediction is introduced as a statement of abductive sort attained by inductive schemes. One of the significant problems concerns unregulated decrease of trusting estimations for regularities obtained during the process of inference organized by analogy with syntax logical systems. Suggested semantic approach generalizes the notion of inference and reveals essential advantages in many aspects without assuming rather strong constraints. In particular, a special set of probabilistic laws is synthesized inductively, this collection has an optimal ability to predict (in the context of available data). Semantic definition of prediction leads us to a new paradigm, where deduction is replaced with computability concept: it rises conditional probability during the steps of inference (in contrast to SLD) and also maximally specifies resulted prediction rule. Moreover, we prove that probabilistic estimations obtained by semantic predictions are greater or equal to those by corresponding SLD-analogical systems. In conclusion practical applications are discussed.

Détail

Keywords: prediction; explanation; probability, logic & learning synthesis; probabilistic logic programming; relational data mining; scientific discovery.