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 paper is a survey of inductive rule learning algorithms that use a separate-and-conquer strategy. This strategy can be traced back to the AQ learning system and still enjoys popularity as can be seen from its frequent use in inductive logic programming systems. We will put this wide variety of algorithms into a single framework and analyze them along three different dimensions, namely their search, language and overfitting avoidance biases.

We present positive PAC-learning results for the nonmonotonic inductive logic programming setting. In particular, we show that first order range-restricted clausal theories that consist of clauses with up to k literals of size at most j each are polynomialsample polynomial-time PAC-learnable with one-sided error from positive examples only. In our framework, concepts are clausal theories and examples are finite interpretations. We discuss the problems encountered when learning theories which only have infinite non-trivial models and propose a way to avoid these problems using a representation change called flattening. Finally, we compare our results to PAC-learnability results for the normal inductive logic programming setting. 1

Inductive Logic Programming (ILP) is a research area which investigates the construction of first-order definite clause theories from examples and background knowledge. ILP systems have been applied successfully in a number of real-world domains. These include the learning of structureactivity rules for drug design, finite-element mesh design rules, rules for primary-secondary prediction of protein structure and fault diagnosis rules for satellites. There is a well established tradition of learning-in-the-limit results in ILP. Recently some results within Valiant's PAC-learning framework have also been demonstrated for ILP systems. In this paper it is argued that algorithms can be directly derived from the formal specifications of ILP. This provides a common basis for Inverse Resolution, ExplanationBased Learning, Abduction and Relative Least General Generalisation. A new general-purpose, efficient approach to predicate invention is demonstrated. ILP is underconstrained by its logical ...

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...

3 -- Akihiro YAMAMOTO y Fachgebiet Intellektik, Fachbereich Informatik Technische Hochschule Darmstadt Alexanderstr. 10, D64283 Darmstadt, GERMANY Phone : +49-6151-16-2863, Fax : +49-6151-16-5326 Email : yamamoto@intellektik.informatik.th-darmstadt.de Abstract In this paper we give a completeness theorem of an inductive inference rule inverse entailment proposed by Muggleton. Our main result is that a hypothesis clause H can be derived from an example E under a background theory B with inverse entailment iff H subsumes E relative to B in Plotkin's sense. The theory B can be any clausal theory, and the example E can be any clause which is neither a tautology nor implied by B. The derived hypothesis H is a clause which is not always definite. In order to prove the result we give declarative semantics for arbitrary consistent clausal theories, and show that SB-resolution, which was originally introduced by Plotkin, is complete procedural semantics. The completeness is shown as ...

Inductive Logic Programming (ILP) has been shown to be a viable approach to many problems in multi-relational data mining (e.g.

Abstract. It is well known that many hard tasks considered in machine learning and data mining can be solved in an rather simple and robust way with an instance- and distance-based approach. In this paper we present another difficult task: learning, from large numbers of performances by concert pianists, to play music expressively. We model the problem as a multi-level decomposition and prediction task. Motivated by structural characteristics of such a task, we propose a new relational distance measure that is a rather straightforward combination of two existing measures. Empirical evaluation shows that our approach is in general viable and our algorithm, named DISTALL, is indeed able to produce musically interesting results. The experiments also provide evidence of the success of ILP in a complex domain such as music performance: it is shown that our instance-based learner operating on structured, relational data outperforms a propositional k-NN algorithm.

. We study the learnability of first order Horn expressions from equivalence and membership queries. We show that the class of range restricted Horn expressions, where every term in the consequent of every clause appears also in the antecedent of the clause, is learnable. The result holds both for the model where interpretations are examples (learning from interpretations) and the model where clauses are examples (learning from entailment). The paper utilises a previous result on learning function free Horn expressions. This is done by using techniques for flattening and unflattening of examples and clauses, and a procedure for model finding for range restricted expressions. This procedure can also be used to solve the implication problem for this class. 1 Introduction We study the problem of exactly identifying universally quantified first order Horn expressions using Angluin's [Ang88] model of exact learning. Much of the work in learning theory has dealt with learning of Boolean exp...

In this paper we discuss how to use SOLresolution, proposed by Inoue, for inductive inference. In order to use some results on Horn clause logic, we define a new inference method SOLD-resolution. SOLD-resolution is obtained by adding the skipping rule to SLD-resolution, and is also regarded as a special type of SOLresolution. When we use SOLD-resolution to hypothesis finding, every derived hypothesis is a negation of a clause, while in induction it must be a clause. We give two solutions to the problem. The first solution is to use inverse entailment proposed by Muggleton. In order to give an inference procedure based on it we add the reducing rule and the saturation rule to SOLD-resolution. The reducing rule is another rule used in SOL-resolution, and saturation is an inference rule proposed by Rouveirol. With our procedure we can derive definite clauses as hypotheses. The second solution is to give a restriction that every hypothesis should be a unit program. Under the restriction we...