Logic approximating sequences of sets

Helena Rasiowa

pp. 167-186

in: Dimiter G. Skordev (ed), Mathematical logic and its applications, Berlin, Springer, 1987

Abstract

In various studies concerning computer science or artificial intelligence, in which approximation tools could be applied, there appears a need of gradual approximating descending set sequences X = (X_m) (e.g. of documents, objects, points) formed of elements satisfying some stronger and stronger conditions. Gradual approximations (both: lower and upper ones) are determined by a descending sequence (≌ _j) of equivalence relations, going to be established progressively. Approximations of grade j+1 are better than those of grade j. Approximations determined by ≌_ω, which is the intersection of ≌_j for j < ω, are the most precise.