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Emrich, M. ) Methodologies for Intelligent Systems, 5: Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems Held 25–27 Oct 1990, pp. 252–259. : Mining big data: current status, and forecast to the future. ACM SIGKDD Explor. Newslett. : Practical implementation of EPLAS: an epistemic programming language for all scientists. In: 2011 international conference on machine learning and cybernetics (ICMLC 2011), pp. 608–616. : From data mining to knowledge discovery in databases.

Let TL(K) be an L-theory with premises K where K ( F(L) is a set of sentences to represent the explicitly known knowledge and/or current beliefs of an agent. , FreeEnCal) is any one of the following operations: or any K, an implicitly epistemic deduction of K, denoted by Kd, is defined as Kd = df TL(K); for any A 62 TL(K) (note that we do not require :A 62 TL(K)), an implicitly epistemic expansion of K by N to deduce A, denoted by TL(K [ N)e+A, is defined as TL(K [ N)e+A = df TL(K [ N) where N ( F(L) such that A 62 TL(K) but A 2 TL(K [ N); in particular, an implicitly epistemic simple-induction is an implicitly epistemic expansion TL(K [ N) e+Vx(A) for Ax(A) 2 TL(K) and an implicitly epistemic abduction is an implicitly epistemic expansion TL(K [ N) e+Vx(A) for C 2 TL(K) and A ) C 2 TL(K) where ) denotes the notion of implication (entailment) in L; for any A 2 TL(K), an implicitly Information Mining for Big Information 35 epistemic contraction of K by N to delete A, denoted by TL(K - N)-A, is defined as TL(K - N)-A = df TL(K - N) where N ( K such that A 62 TL(K - N), in particular, an implicitly epistemic consistent-contraction is an implicitly epistemic contraction TL(K - N)-A for :A 2 TL(K) or TL(K - N)-A for A 2 TL(K).

By using deductive reasoning, analysts can check the proposition systematically. Doing information deduction is just deductive reasoning. Inductive reasoning is a way of information abstraction. Similarly, abductive reasoning is a way of hypothesis generation. 2 Formal Logic System and Formal Theory To accept results of consistency verification, hypothesis generation, and information deduction with deductive reasoning as correct ones, deductive reasoning should be a logically valid reasoning. When doing deductive reasoning, deduced conclusions should be true if premises are true, and that the conclusions should be related to the premises.