Current norm-based automatic termination analysis techniques for logic programs can be split up into different components: inference of mode or type information, derivation of models, generation of well-founded orders, and verification of the termination conditions themselves. Although providing high-precision results, these techniques suffer from an efficiency point of view, as several of these analyses are often performed through abstract interpretation. We present a new termination analysis which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs. The proposed method is both efficient and precise. The use of constraint sets enables the propagation of information over all different phases while the need for multiple analyses is considerably reduced.

Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end, the notion of a query pack is introduced: it structures sets of similar queries. Furthermore, a mechanism is described for executing such query packs. A complexity analysis shows that considerable efficiency improvements can be achieved through the use of this query pack execution mechanism. This claim is supported by empirical results obtained by incorporating support for query pack execution in two existing learning systems.

In the domain of crystal engineering, various schemes have been proposed for the classification of hydrogen bonding (H-bonding) patterns observed in 3D crystal structures. In this study, the aim is to complement these schemes with rules that predict H-bonding in crystals from 2D structural information only. Modern computational power and the advances in inductive logic programming (ILP) can now provide computational chemistry with the opportunity for extracting structure-specific rules from large databases that can be incorporated into expert systems. ILP technology is here applied to H-bonding in crystals to develop a self-extracting expert system utilizing data in the Cambridge Structural Database of small molecule crystal structures. A clear increase in performance was observed when the ILP system DMax was allowed to refer to the local structural environment of the possible H-bond donor/acceptor pairs. This ability distinguishes ILP from more traditional approaches that build rules on the basis of global molecular properties.

In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of methods to prove the absence of a solution. Considering the definite program and the query ← Q as clauses of a first order theory, one can apply model generators which search for a finite interpretation in which the program clauses as well as the clause false ← Q are true. This paper develops a new approach which exploits the fact that all clauses are definite. It is based on a goal directed abductive search in the space of finite pre-interpretations for a pre-interpretation such that Q is false in the least model of the program based on it. Several methods for efficiently searching the space of pre-interpretations are presented. Experimental results confirm that our approach find solutions with less search than with the use of a first order model generator.In what follows, we give some results formalising the relationship between a program and its abstraction. First, we introduce some notational conventions. With Cl a clause, Cl a denotes its abstraction; with P a set of clauses (a program), P a denotes its abstraction. J a is the Herbrand pre-interpretation of P a ∪ P a J . Remark that J a has the same domain as J as the domain elements are the only functors in P a ∪ P a J . I J denotes the interpretation which is the least Herbrand model of P a J . Finally, I a is the interpretation of P a ∪ P a J corresponding to the interpretation I when I a = I ∪ I J .Theorem 1. Let I be an interpretation of P based on pre-interpretation J and I a the corresponding interpretation of P a ∪ P a J . The interpretation I is a model of P ∪ {false ← Q} iff I a is a model of P a ∪ P a J ∪ {false ← Q a }.