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

GAMoN: Discovering M-of-N{¬,∨} hypotheses for text classification by a lattice-based Genetic Algorithm

AbstractWhile there has been a long history of rule-based text classifiers, to the best of our knowledge no M-of-N-based approach for text categorization has so far been proposed. In this paper we argue that M-of-N hypotheses are particularly suitable to model the text classification task because of the so-called “family resemblance” metaphor: “the members (i.e., documents) of a family (i.e., category) share some small number of features, yet there is no common feature among all of them. Nevertheless, they resemble each other”. Starting from this conjecture, we provide a sound extension of the M-of-N approach with negation and disjunction, called M-of-N{¬,∨}, which enables to best fit the true structure of the data. Based on a thorough theoretical study, we show that the M-of-N{¬,∨} hypothesis space has two partial orders that form complete lattices.GAMoN is the task-specific Genetic Algorithm (GA) which, by exploiting the lattice-based structure of the hypothesis space, efficiently induces accurate M-of-N{¬,∨} hypotheses.Benchmarking was performed over 13 real-world text data sets, by using four rule induction algorithms: two GAs, namely, BioHEL and OlexGA, and two non-evolutionary algorithms, namely, C4.5 and Ripper. Further, we included in our study linear SVM, as it is reported to be among the best methods for text categorization. Experimental results demonstrate that GAMoN delivers state-of-the-art classification performance, providing a good balance between accuracy and model complexity. Further, they show that GAMoN can scale up to large and realistic real-world domains better than both C4.5 and Ripper

Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems such as $\mathcal{AL}$-log that integrates the description logic $\mathcal{ALC}$ and the function-free Horn clausal language \textsc{Datalog}. In this paper we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of $\mathcal{AL}$-log. The framework is valid whatever the scope of induction (description vs. prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement. Keywords: Inductive Logic Programming, Hybrid Knowledge Representation and Reasoning Systems, Ontologies, Semantic Web. Note: To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 6 figure

Joining implications in formal contexts and inductive learning in a Horn description logic: Extended Version

A joining implication is a restricted form of an implication where it is explicitly specified which attributesmay occur in the premise and in the conclusion, respectively. A technique for sound and complete axiomatization of joining implications valid in a given formal context is provided. In particular, a canonical base for the joining implications valid in a given formal context is proposed, which enjoys the property of being of minimal cardinality among all such bases. Background knowledge in form of a set of valid joining implications can be incorporated. Furthermore, an application to inductive learning in a Horn description logic is proposed, that is, a procedure for sound and complete axiomatization of Horn-M concept inclusions from a given interpretation is developed. A complexity analysis shows that this procedure runs in deterministic exponential time

Most specific consequences in the description logic EL

The notion of a most specific consequence with respect to some terminological box is introduced, conditions for its existence in the description logic EL and its variants are provided, and means for its computation are developed. Algebraic properties of most specific consequences are explored. Furthermore, several applications that make use of this new notion are proposed and, in particular, it is shown how given terminological knowledge can be incorporated in existing approaches for the axiomatization of observations. For instance, a procedure for an incremental learning of concept inclusions from sequences of interpretations is developed

Confinement for active objects

In this paper, we provide a formal framework for the security of distributed active objects. Active objects communicate asynchronously implementing method calls via futures. We base the formal framework on a security model that uses a semi-lattice to enable multi-lateral security crucial for distributed architectures. We further provide a security type system for the programming model ASPfun of functional active objects. Type safety and a confinement property are presented. ASPfun thus realizes secure down calls