Applying MML to ILP ∗

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, ∗This work has been partially supported by the EU (FEDER) and the Spanish MEC under grant TIN 2004-7943-C04-02, Generalitat Valenciana under grant GV06/301 and UPV under grant TAMAT. †C. Ferri was supported by grant 2765 of UPV during a stay at Monash University. namely the model complexity and proof complexity approaches.