Completeness and properness of refinement operators in inductive logic programming

AbstractWithin Inductive Logic Programming, refinement operators compute a set of specializations or generalizations of a clause. They are applied in model inference algorithms to search in a quasi-ordered set for clauses of a logical theory that consistently describes an unknown concept. Ideally, a refinement operator is locally finite, complete, and proper. In this article we show that if an element in a quasi-ordered set 〈S, ≥〉 has an infinite or incomplete cover set, then an ideal refinement operator for 〈S, ≥〉 does not exist. We translate the nonexistence conditions to a specific kind of infinite ascending and descending chains and show that these chains exist in unrestricted sets of clauses that are ordered by θ-subsumption. Next we discuss how the restriction to a finite ordered subset can enable the construction of ideal refinement operators. Finally, we define an ideal refinement operator for restricted θ-subsumption ordered sets of clauses

Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables

Logic-based machine learning using a bounded hypothesis space: the lattice structure, refinement operators and a genetic algorithm approach

Rich representation inherited from computational logic makes logic-based machine learning a competent method for application domains involving relational background knowledge and structured data. There is however a trade-off between the expressive power of the representation and the computational costs. Inductive Logic Programming (ILP) systems employ different kind of biases and heuristics to cope with the complexity of the search, which otherwise is intractable. Searching the hypothesis space bounded below by a bottom clause is the basis of several state-of-the-art ILP systems (e.g. Progol and Aleph). However, the structure of the search space and the properties of the refinement operators for theses systems have not been previously characterised. The contributions of this thesis can be summarised as follows: (i) characterising the properties, structure and morphisms of bounded subsumption lattice (ii) analysis of bounded refinement operators and stochastic refinement and (iii) implementation and empirical evaluation of stochastic search algorithms and in particular a Genetic Algorithm (GA) approach for bounded subsumption. In this thesis we introduce the concept of bounded subsumption and study the lattice and cover structure of bounded subsumption. We show the morphisms between the lattice of bounded subsumption, an atomic lattice and the lattice of partitions. We also show that ideal refinement operators exist for bounded subsumption and that, by contrast with general subsumption, efficient least and minimal generalisation operators can be designed for bounded subsumption. In this thesis we also show how refinement operators can be adapted for a stochastic search and give an analysis of refinement operators within the framework of stochastic refinement search. We also discuss genetic search for learning first-order clauses and describe a framework for genetic and stochastic refinement search for bounded subsumption. on. Finally, ILP algorithms and implementations which are based on this framework are described and evaluated.Open Acces

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Similarity measures over refinement graphs

Similarity also plays a crucial role in support vector machines. Similarity assessment plays a key role in lazy learning methods such as k-nearest neighbor or case-based reasoning. In this paper we will show how refinement graphs, that were originally introduced for inductive learning, can be employed to assess and reason about similarity. We will define and analyze two similarity measures, S λ and S π, based on refinement graphs. The anti-unification-based similarity, S λ, assesses similarity by finding the anti-unification of two instances, which is a description capturing all the information common to these two instances. The property-based similarity, S π, is based on a process of disintegrating the instances into a set of properties, and then analyzing these property sets. Moreover these similarity measures are applicable to any representation language for which a refinement graph that satisfies the requirements we identify can be defined. Specifically, we present a refinement graph for feature terms, in which several languages of increasing expressiveness can be defined. The similarity measures are empirically evaluated on relational data sets belonging to languages of different expressiveness. © 2011 The Author(s).Support for this work came from the project Next-CBR TIN2009-13692-C03-01 (co-sponsored by EU FEDER funds)Peer Reviewe

On avoiding redundancy in inductive logic programming

ILP systems induce rst-order clausal theories performing asearch through very large hypotheses spaces containing redundant hypotheses.The generation of redundant hypotheses may prevent the systemsfrom nding good models and increases the time to induce them.In this paper we propose a classication of hypotheses redundancy andshow how expert knowledge can be provided to an ILP system to avoidit. Experimental results show that the number of hypotheses generatedand execution time are reduced when expert knowledge is used to avoidredundancy

Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

Inductive Logic Programming considers almost exclusively universally quantied theories. To add expressiveness, prenex conjunctive normal forms (PCNF) with existential variables should also be considered. ILP mostly uses learning with refinement operators. To extend refinement operators to PCNF, we should first do so with substitutions. However, applying a classic substitution to a PCNF with existential variables, one often obtains a generalization rather than a specialization. In this article we define substitutions that specialize a given PCNF and a weakly complete downward refinement operator. Moreover, we analyze the complexities of this operator in different types of languages and search spaces. In this way we lay a foundation for learning systems on PCNF. Based on this operator, we have implemented a simple learning system PCL on some type of PCNF

As lazy as it can be

Inductive Logic Programming (ILP) is a promising technology for knowledgeextraction applications. ILP has produced intelligible solutions for a wide variety of domains where it has been applied. The ILP lack of efficiency is, however, a major impediment for its scalability to applications requiring large amounts of data. In this paper we address important issues that must be solved to make ILP scalable to applicationsof knowledge extraction in large amounts of data. The issues include: efficiency and storage requirements.We propose and evaluate a set of techniques, globally called lazy evaluation of examples, to improve the efficiency of ILP systems. Lazy evaluation is essentially a way to avoid or postpone the evaluation of the generated hypotheses (coverage tests). To reduce the storage amount a representation schema called interval trees is proposed and evaluated.All the techniques were evaluated using the IndLog ILP system and a set of ILPdatasets referenced in the literature. The proposals lead to substantial efficiency improvements and memory savings and are generally applicable to any ILP system