Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic context-free grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a first-order range-restricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform probability labels on each definition and near-maximal Bayes posterior probability and then 2) alters the probability labels to further increase the posterior probability. Stage 1) is implemented within CProgol4.5, which differs from previous versions of Progol by allowing user-defined evaluation functions written in Prolog. It is shown that maximising the Bayesian posterior function involves nding SLPs with short derivations of the examples. Search pruning with the Bayesian evaluation function is carried out in the same way as in previous versions of CProgol. The system is demonstrated with worked examples involving the learning of probability distributions over sequences as well as the learning of simple forms of uncertain knowledge.

Abstract. This paper describes FOIL, a system that learns Horn clauses from data expressed as relations. FOIL is based on ideas that have proved effective in attribute-value learning systems, but extends them to a first-order formalism. This new system has been applied successfully to several tasks taken from the machine learning literature.

: FOIL is a learning system that constructs Horn clause programs from examples. This paper summarises the development of FOIL from 1989 up to early 1993 and evaluates its effectiveness on a non-trivial sequence of learning tasks taken from a Prolog programming text. Although many of these tasks are handled reasonably well, the experiment highlights some weaknesses of the current implementation. Areas for further research are identified. 1. Introduction The principal differences between zeroth-order and first-order supervised learning systems are the form of the training data and the way that a learned theory is expressed. Data for zeroth-order learning programs such as ASSISTANT [Cestnik, Kononenko and Bratko, 1986], CART [Breiman, Friedman, Olshen and Stone, 1984], CN2 [Clark and Niblett, 1987] and C4.5 [Quinlan, 1992] comprise preclassified cases, each described by its values for a fixed collection of attributes. These systems develop theories, in the form of decision trees o...

Knowledge acquisition is a difficult, error-prone, and time-consuming task. The task of automatically improving an existing knowledge base using learning methods is addressed by the class of systems performing theory refinement. This paper presents a system, Forte (First-Order Revision of Theories from Examples), which refines first-order Horn-clause theories by integrating a variety of different revision techniques into a coherent whole. Forte uses these techniques within a hill-climbing framework, guided by a global heuristic. It identifies possible errors in the theory and calls on a library of operators to develop possible revisions. The best revision is implemented, and the process repeats until no further revisions are possible. Operators are drawn from a variety of sources, including propositional theory refinement, first-order induction, and inverse resolution. Forte is demonstrated in several domains, including logic programming and qualitative modelling.

Abstract. When comparing inductive logic programming (ILP) and attribute-value learning techniques, there is a trade-off between expressive power and efficiency. Inductive logic programming techniques are typically more expressive but also less efficient. Therefore, the data sets handled by current inductive logic programming systems are small according to general standards within the data mining community. The main source of inefficiency lies in the assumption that several examples may be related to each other, so they cannot be handled independently. Within the learning from interpretations framework for inductive logic programming this assumption is unnecessary, which allows to scale up existing ILP algorithms. In this paper we explain this learning setting in the context of relational databases. We relate the setting to propositional data mining and to the classical ILP setting, and show that learning from interpretations corresponds to learning from multiple relations and thus extends the expressiveness of propositional learning, while maintaining its efficiency to a large extent (which is not the case in the classical ILP setting). As a case study, we present two alternative implementations of the ILP system Tilde (Top-down Induction of Logical DEcision trees): Tildeclassic, which loads all data in main memory, and TildeLDS, which loads the examples one by one. We experimentally compare the implementations, showing TildeLDS can handle large data sets (in the order of 100,000 examples or 100 MB) and indeed scales up linearly in the number of examples.

We present the learning system Maccent which addresses the novel task of stochastic MAximum ENTropy modeling with Clausal Constraints. Maximum Entropy method is a Bayesian method based on the principle that the target stochastic model should be as uniform as possible, subject to known constraints. Maccent incorporates clausal constraints that are based on the evaluation of Prolog clauses in examples represented as Prolog programs. We build on an existing maximum-likelihood approach to maximum entropy modeling, which we upgrade along two dimensions: (1) Maccent can handle larger search spaces, due to a partial ordering defined on the space of clausal constraints, and (2) uses a richer firstorder logic format. In comparison with other inductive logic programming systems, Maccent seems to be the first that explicitly constructs a conditional probability distribution p(CjI) based on an empirical distribution ~ p(CjI) (where p(CjI) (~p(CjI)) gives the induced (observed) probability of ...

This paper presents an algorithm that combines traditional EBL techniques and recent developments in inductive logic programming to learn effective clause selection rules for Prolog programs. When these control rules are incorporated into the original program, significant speed-up may be achieved. The algorithm is shown to be an improvement over competing EBL approaches in several domains. Additionally, the algorithm is capable of automatically transforming some intractable algorithms into ones that run in polynomial time. 1 Introduction Explanation-based learning (EBL) research in logic programming has generally focussed on learning macros (compiled rules) [ Mitchell et al., 1986; DeJong and Mooney, 1986; Prieditis and Mostow, 1987 ] , while EBL work in planning and production systems has tended to focus on learning search-control rules [ Minton, 1988; Laird et al., 1986 ] . Recently, Cohen [ Cohen, 1990 ] has argued the advantages of learning search control rules for the clause se...

Model-based reasoning about a system requires an explicit representation of the system's components and their connections. Diagnosing such a system consists of locating those components whose abnormal behavior accounts for the faulty system behavior. In order to increase the efficiency of model-based diagnosis, we propose a model representation at several levels of detail, and define three refinement (abstraction) operators. We specify formal conditions that have to be satisfied by the hierarchical representation, and emphasize that the multi-level scheme is independent of any particular single-level model representation. The hierarchical diagnostic algorithm which we define turns out to be very general. We show that it emulates the bisection method, and can be used for hierarchical constraint satisfaction. We apply the hierarchical modeling principle and diagnostic algorithm to a medium-scale medical problem. The performance of a four-level qualitative model of the heart is compared t...

Top-down induction of decision trees (TDIDT) is a very popular machine learning technique. Up till now, it has mainly been used for propositional learning, but seldomly for relational learning or inductive logic programming. The main contribution of this paper is the introduction of logical decision trees, which make it possible to use TDIDT in inductive logic programming. An implementation of this top-down induction of logical decision trees, the Tilde system, is presented and experimentally evaluated. 1

Within KDD, the discovery of frequent patterns has been studied in a variety of settings. In its simplest form, known from association rule mining, the task is to discover all frequent item sets, i.e., all combinations of items that are found in a sufficient number of examples.