Theta-Subsumption in a Constraint Satisfaction Perspective

The covering test intensively used in Inductive Logic Programming, i.e. θ-subsumption, is formally equivalent to a Constraint Satisfaction problem (CSP). This paper presents a general reformulation of θ-subsumption into a binary CSP, and a new θ-subsumption algorithm, termed Django, which combines some main trend CSP heuristics and other heuristics specifically designed for θ-subsumption. Django is evaluated after the CSP standards, shifting from a worst-case complexity perspective to a statistical framework, centered on the notion of Phase Transition (PT). In the PT region lie the hardest on average CSP instances; and this region has been shown of utmost relevance to ILP [4]. Experiments on artificial θ-subsumption problems designed to illustrate the phase transition phenomenon, show that Django is faster by several orders of magnitude than previous θ-subsumption algorithms, within and outside the PT region.