The Justi£cation Problem of Data Mining — A Decision Logic Formulation and Its Implications

Data mining is an instance of the inductive methodology. Many philosophical considerations for induction can also be carried out for data mining. In particular, the justi£cation of induction has been a long-standing problem in epistemology. This article is a recast of the problem in the context of data mining. We formulate the problem precisely in the rough set-based decision logic and discuss its implications for the research of data mining. 1 The Circular Justi£cation of Induction Induction is widely accepted as a cornerstone of the modern scienti£c methodology. It regards the systematic use of past experiences in the prediction of the future. According to Hume’s epistemology, our beliefs are established on the basis of observation and can be divided into two cases: 1. Observed matters of fact. 2. Unobserved matters of fact. While the beliefs of observed matters of fact are based directly on observation, unobserved matters of fact can only be known indirectly on the basis of observation by means of inductive argument. An argument is called inductive if it passes from singular statements regarding the results of observations to universal statements, such as hypotheses or theories. The inductive argument can be formulated deductively as follows: Let φ(x) denote a hypothesis regarding the individuals x we are interested in. In general, φ(x) is in the form of a universal conditional sentence “P (x) ⊃ Q(x)”, however it is not necessarily so. Let Φ and Ψ denote the following sentences Φ : φ(x) holds for all observed x. Department of Information Engineering, National Penghu Institute of Technology, Penghu, Taiwan. Email: [email protected] Institute of Information Science, Academia Sinica, Taipei, Taiwan. Email: [email protected]. Ψ: φ(x) holds for all x (or at least the next observed x). Then the inductive argument is just an application of the modus ponens rule and can be expressed as