Summary: [For the entire collection see Zbl 0752.00047.] As was noted by {\it M. Pittarelli} [Int. J. Gen. Syst. 15, No. 1, 1-58 (1989; Zbl 0675.93070)], statistical model search techniques suggested by {\it D. Edwards} and the author [Biometrika 72, 339-351 (1985; Zbl 0576.62067)] can be applied for solving some problems in reconstructability analysis as considered by {\it R. E. Cavallo} and {\it G. J. Klir} [Int. J. Gen. Syst. 7, 7-32 (1981; Zbl 0464.93009) and ibid. 5, 143-171 (1979; Zbl 0458.93003)]. These techniques are oriented towards approximations of a multivariate discrete distribution by distributions satisfying restrictions concerning e.g. some independence assumptions. The relevance of this approach to the problem of constructing a probabilistic knowledge base will be discussed, namely in connection with the coherence of uncertainty measures (distances) with respect to a simplicity ordering between discrete distributions.