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.

This paper firstly provides a re-appraisal of the development of techniques for inverting deduction, secondly introduces Mode-Directed Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol is implemented in C and available by anonymous ftp. The re-assessment of previous techniques in terms of inverse entailment leads to new results for learning from positive data and inverting implication between pairs of clauses.

All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising first-order clauses have involved inverting the clausal subsumption relationship. However, even Plotkin realised that this approach was incomplete. Since inversion of subsumption is central to many Inductive Logic Programming approaches, this form of incompleteness has been propagated to techniques such as Inverse Resolution and Relative Least General Generalisation. A more complete approach to inverting implication has been attempted with some success recently by Lapointe and Matwin. In the present paper the author derives general solutions to this problem from first principles. It is shown that clausal subsumption is only incomplete for self-recursive clauses. Avoiding this incompleteness involves algorithms which find "nth roots" of clauses. Completeness and correctness results are proved for a non-deterministic algorithms which constructs nth ro...

Inductive Logic Programming (ILP) involves the synthesis of logic programs from examples. In terms of scientific theory formation ILP systems define observational predicates in terms of a set of theoretical predicates. However, certain basic theorems indicate that with an inadequate theoretical vocabulary this is not always possible. Predicate invention is the augmentation of a given theoretical vocabulary to allow finite axiomatisation of the observational predicates. New theoretical predicates need to be chosen from a well defined universe of such predicates. In this paper a partial order of utilisation is described over such a universe. This ordering is a special case of a logical translation. The notion of utilisation allows the definition of an equivalence relationship over new predicates. In a manner analogous to Plotkin clause refinement is defined relative to given background knowledge and a universe of new predicates. It is shown that relative least clause refinement is define...