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.

This thesis is about inductive learning, or learning from examples. The goal has been to investigate ways of improving learning algorithms. The chess end-game "King and Rook against King" (KRK) was chosen, and a number of benchmark learning tasks were defined within this domain, sufficient to over-challenge stateof -the-art learning algorithms. The tasks comprised learning rules to distinguish (1) illegal positions and (2) legal positions won optimally in a fixed number of moves. From our experimental results with task (1) the best-performing algorithm was selected and a number of improvements were made. The principal extension to this generalisation method was to alter its representation from classical logic to a non-monotonic formalism. A novel algorithm was developed in this framework to implement rule specialisation, relying on the invention of new predicates. When experimentally tested this combined approach did not at first deliver the expected performance gains due to restrictio...

This paper discusses the generalization of definite Horn programs beyond the ordering of logical implication. Since the seminal paper on generalization of clauses based on ` subsumption, there are various extensions in this area. Especially in inductive logic programming(ILP), people are using various methods that approximate logical implication, such as inverse resolution(IR), relative least general generalization(RLGG), and inverse implication(II), to generalize clauses. However, the logical implication is not the most desirable form of generalization. A program is more general than another program does not necessarily mean that the former should logically imply the latter. Instead, a more natural notion of generalization is the set inclusion ordering on the success set of logic programs. We observe that this kind of generalization relation is especially useful for inductive synthesis of logic programs. In this paper, we first define an ordering between logic programs which is strict...

. This paper studies the properties of inverse resolution in normal logic programs. The V-operators are known as operations for inductive generalization in definite logic programs. In the presence of negation as failure in a program, however, the V-operators do not work as generalization operations in general and often make a consistent program inconsistent. Moreover, they may destroy the syntactic structure of logic programs such as acyclicity and local stratification. On the procedural side, unrestricted application of the V-operators may lose answers computed in the original program and make queries flounder. We provide su#cient conditions for the V-operators to avoid these problems. 1 Introduction Inverse resolution introduced in [13] is known as operations which perform inductive generalization in definite logic programs. There are two operators that carry out inverse resolution, absorption and identification, which are called the V-operators together. Each operator builds one o...

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Belief change is concerned with modelling the way in which a rational reasoner maintains its beliefs as it acquires new information. Of particular interest is the way in which new beliefs are acquired and determined and old beliefs are retained or discarded. A parallel can be drawn to symbolic machine learning approaches where examples to be categorised are presented to the learning system and a theory is subsequently derived, usually over a number of iterations. It is therefore not surprising that the term ‘theory revision ’ is used to describe this process [Ourston and Mooney, 1994]. Viewing a machine learning system as a rational reasoner allows us to begin seeing these seemingly disparate mechanisms