. In this paper we argue that the use of a language with a type system, together with higher-order facilities and functions, provides a suitable basis for knowledge representation in inductive concept learning and, in particular, illuminates the relationship between attribute-value learning and inductive logic programming (ILP). Individuals are represented by closed terms: tuples of constants in the case of attribute-value learning; arbitrarily complex terms in the case of ILP. To illustrate the point, we take some learning tasks from the machine learning and ILP literature and represent them in Escher, a typed, higher-order, functional logic programming language being developed at the University of Bristol. We argue that the use of a type system provides better ways to discard meaningless hypotheses on syntactic grounds and encompasses many ad hoc approaches to declarative bias. 1. Motivation and scope Inductive concept learning consists of finding mappings of individuals (or objects...

. We present a novel application of inductive logic programming (ILP) in the area of quantitative structure-activity relationships (QSARs). The activity we want to predict is the biodegradability of chemical compounds in water. In particular, the target variable is the half-life in water for aerobic aqueous biodegradation. Structural descriptions of chemicals in terms of atoms and bonds are derived from the chemicals' SMILES encodings. Definition of substructures are used as background knowledge. Predicting biodegradability is essentially a regression problem, but we also consider a discretized version of the target variable. We thus employ a number of relational classification and regression methods on the relational representation and compare these to propositional methods applied to different propositionalisations of the problem. Some expert comments on the induced theories are also given. 1 Introduction The persistence of chemicals in the environment (or to environmen...

A novel first order clustering system, called C 0.5, is presented. It inherits its logical decision tree formalism from the TILDE system, but instead of using class information to guide the search, it employs the principles of instance based learning in order to perform clustering. Various experiments are discussed, which show the promise of the approach. 1 Introduction A decision tree is usually seen as representing a theory for classification of examples. If the examples are positive and negative examples for one specific concept, then the tree defines these two concepts. One could also say, if there are k classes, that the tree defines k concepts. Another viewpoint is taken in Langley's Elements of Machine Learning [ Langley, 1996 ] . Langley sees decision tree induction as a special case of the induction of concept hierarchies. A concept is associated with each node of the tree, and as such the tree represents a kind of taxonomy, a hierarchy of many concepts. This is very similar...

We investigate how abduction and induction can be integrated into a common learning framework through the notion of Abductive Concept Learning (ACL). ACL is an extension of Inductive Logic Programming (ILP) to the case in which both the background and the target theory are abductive logic programs and where an abductive notion of entailment is used as the coverage relation. In this framework, it is then possible to learn with incomplete information about the examples by exploiting the hypothetical reasoning of abduction. The paper presents the basic framework of ACL with its main characteristics and illustrates its potential in addressing several problems in ILP such as learning with incomplete information and multiple predicate learning. An algorithm for ACL is developed by suitably extending the top-down ILP method for concept learning and integrating this with an abductive proof procedure for Abductive Logic Programming (ALP). A prototype system has been developed and applied to lea...

. In this paper, we indicate some possible applications of ILP or similar techniques in the knowledge discovery field, and then discuss several methods for adapting and linking ILP-systems to relational database systems. The proposed methods range from "pure ILP" to "based on techniques originating in ILP". We show that it is both easy and advantageous to adapt ILP-systems in this way. 1 Introduction It is common knowledge that in the machine learning field, ILP has turned out to be very useful for classification problems in structured domains. Similar problems can be found in the knowledge discovery field. For instance, finding integrity constraints holding in a database closely corresponds to finding classification rules with ILP, as we will show later on in this paper. In the past, research on knowledge discovery in databases (KDD) has focused mainly on propositional techniques; this implies that relationships between the attributes of one tuple can be found, but no relationships b...

Inductive logic programming systems usually send large numbers of queries to a database. The lattice structure from which these queries are typically selected causes many of these queries to be highly similar. As a consequence, independent execution of all queries may involve a lot of redundant computation. We propose a mechanism for executing a hierarchically structured set of queries (a "query pack") through which a lot of redundancy in the computation is removed. We have incorporated our query pack execution mechanism in the ILP systems Tilde and Warmr by implementing a new Prolog engine ilProlog which provides support for pack execution at a lower level. Experimental results demonstrate significant efficiency gains. Our query pack execution mechanism is very general in nature and could be incorporated in most other ILP systems, with similar efficiency improvements to be expected.

The task of discovering interesting regularities in (large) sets of data (data mining, knowledge discovery) has recently met with increased interest in Machine Learning in general and in Inductive Logic Programming (ILP) in particular. However, while there is a widely accepted definition for the task of concept learning from examples in ILP, definitions for the data mining task have been proposed only recently. In this paper, we examine these so-called "nonmonotonic semantics" definitions and show that non-monotonicity is only an incidental property of the data mining learning task, and that this task makes perfect sense without such an assumption. We therefore introduce and define a generalized definition of the data mining task called the ILP description learning problem and discuss its properties and relation to the traditional concept learning (prediction) learning problem. Since our characterization is entirely on the level of models, the definition applies independently of the ch...

We investigate how abduction and induction can be integrated into a common learning framework. In particular, we consider an extension of Inductive Logic Programming (ILP) for the case in which both the background and the target theories are abductive logic programs and where an abductive notion of entailment is used as the basic coverage relation for learning. This extended learning framework has been called Abductive Concept Learning (ACL). In this framework, it is possible to learn with incomplete background information about the training examples by exploiting the hypothetical reasoning of abduction. We also study how the ACL framework can be used as a basis for multiple predicate learning. An algorithm for ACL is developed by suitably extending the topdown ILP method: the deductive proof procedure of Logic Programming is replaced by an abductive proof procedure for Abductive Logic Programming. This algorithm also incorporates a phase for learning integrity 2 Fabrizio...

Many learning systems, e.g. systems based on clustering and instance based learning systems, need a measure for the distance between objects. Adequate measures are available for attribute value learners. In recent years there is a growing interest in first order learners, however existing proposals for distances between non-ground atoms have some drawbacks. In this paper we develop a new measure for the distance between nonground atoms. 1 Introduction In learning systems based on clustering (e.g. C0.5 [3], KBG [1]) and in instance based learning (e.g. [9, ch.4], RIBL [6]), a measure of the distance between objects is an essential component. Good measures exist for distances between objects in an attribute value representation (see e.g. [9, ch. 4]). Recently there is a growing interest in using more expressive first order representations of objects and in upgrading propositional learning systems into first order learning systems (e.g. TILDE [2], ICL [5] and CLAUDIEN [4]). Some ad-hoc s...

Three companion systems, Claudien, ICL and Tilde, are presented. They use a common representation for examples and hypotheses: each example is represented by a relational database. This contrasts with the classical inductive logic programming systems such as Progol and Foil. It is argued that this representation is closer to attribute value learning and hence more natural. Furthermore, the three systems can be considered first order upgrades of typical data mining systems, which induce association rules, classification rules or decision trees respectively. 1