this paper is to describe some of the relationships among the different streams and to try to clarify some of the important differences in their assumptions and development. Other studies mentioning the relationships appear in [1, Section IV, pp. 1038--1039], [2, sections 5.2, 5.5] and [3, p. 465]

this paper is given in [DADH95] and is available from ftp://www.cs.monash.edu.au/www/publications/1995/TR237.ps.Z.) Section 2introduces the MML principle and how it can be used for this circular clustering problem. The remaining sections give the results of the secondary structure groups [KaSa83] that resulted from applying Snob to cluster our dihedral angle data.

In Inductive Logic Programming (ILP), since logic is a complete (universal) language, innitely many possible hypotheses are compatible (hence plausible) given the evidence. An intrinsic way of selecting the most convenient hypothesis from the set of possible theories is not only useful for model selection but it is also useful for guiding the search in the hypotheses space, as some ILP systems have done in the past. One selection/search criterion is to apply Occam's razor, i.e. to rst select/try the simplest hypotheses which cover the evidence. In order to do this, it is necessary to measure how simple a theory is. The Minimum Message Length (MML) principle is based on information theory and it re ects Occam's razor philosophy. In this paper we present a MML method for costing both logic programs and sets of facts according to the theory. Our scheme has a solid foundation and avoids the drawbacks of previous coding schemes in ILP,