By E. (Edmond) Ramis, C. (Claude) Deschamps, J Odoux

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T o . • • ·----~2 Figure 2. For any ke {l, .. e. U can be distinguished from w by formula cI> with depth not greater than n+ 1, therefore (u,w) e On+1 = On = On+{, a contradiction. o The idea of the lemma is illustrated on Figure 2. Now we can construct an algorithm generating all the pairs that are distinguishable. 2 Procedure Analysis begin Compute (Do); n :=0; repeat n :;=n+l; Compute(DJ until Dn = Dn-1 end. Application Using procedure Analysis one can easily solve the following problems: • Problem 1: For a given Kripke model ~ = (W, {Rm}meM, val) and states u,we W check if there exists a formula which distinguishes u from w.

Wasilewska, A and Vigneron, L. (1995) Rough equality algebras. Proceedings of the Annual Joint Conference on Information Sciences, Wrightsville Beach, North Carolina, USA. 26-30. Wasilewska, A and Vigneron, L. (1996) Rough and modal algebras. Proceedings of CESA'96 IMACS Multiconference: Computational Engineering in Systems Applications, Lille, France. Vol. I, 123-130. Wasilewska, A and Vigneron, L. (1997) Rough R4 and R5 algebras. International Journal of Information Sciences, to appear. Wedberg, A (1948) The Aristotelian theory of classes.

The final decision is the one with the greatest number nlvJ, more precisely, it is chosen randomly from the set {j: n;(v)= maxi ni(v)}. In our system we have also implemented some other general strategies for classifying new objects. Among them there is the following one. From the original decision table A a set of subtables is created. Any subtable corresponds to a dynamic reduct (with the stability coefficient greater than a given threshold). Next, we generate a family of sets of decision rules for these subtables with minimal number of descriptors.