Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We present YAGO, a light-weight and extensible ontology with high coverage and quality. YAGO builds on entities and relations and currently contains more than 1 million entities and 5 million facts. This includes the Is-A hierarchy as well as non-taxonomic relations between entities (such as HASONEPRIZE). The facts have been automatically extracted from Wikipedia and unified with WordNet, using a carefully designed combination of rule-based and heuristic methods described in this paper. The resulting knowledge base is a major step beyond WordNet: in quality by adding knowledge about individuals like persons, organizations, products, etc. with their semantic relationships - and in quantity by increasing the number of facts by more than an order of magnitude. Our empirical evaluation of fact correctness shows an accuracy of about 95%. YAGO is based on a logically clean model, which is decidable, extensible, and compatible with RDFS. Finally, we show how YAGO can be further extended by state-of-the-art information extraction techniques.

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Yago: a core of semantic knowledge

https://www.cs.ox.ac.uk/people/bernardo.cuencagrau/publications/PelletDemo.pdf

Pellet: A practical OWL-DL reasoner

Data integration is the problem of combining data residing at different sources, and providing the user with a unified view of these data. The problem of designing data integration systems is important in current real world applications, and is characterized by a number of issues that are interesting from a theoretical point of view. This document presents on overview of the material to be presented in a tutorial on data integration. The tutorial is focused on some of the theoretical issues that are relevant for data integration. Special attention will be devoted to the following aspects: modeling a data integration application, processing queries in data integration, dealing with inconsistent data sources, and reasoning on queries.

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Data integration: a theoretical perspective

Formal Concept Analysis

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. In a recent paper, we have shown that unification in \(\mathcal{EL}\) is NP-complete, and thus of a complexity that is considerably lower than in other Description Logics of comparably restricted expressive power. In this paper, we introduce a new NP-algorithm for solving unification problems in \(\mathcal{EL}\), which is based on a reduction to satisfiability in propositional logic (SAT). The advantage of this new algorithm is, on the one hand, that it allows us to employ highly optimized state-of-the-art SAT solvers when implementing an \(\mathcal{EL}\)-unification algorithm. On the other hand, this reduction provides us with a proof of the fact that \(\mathcal{EL}\)-unification is in NP that is much simpler than the one given in our previous paper on \(\mathcal{EL}\)-unification.

SAT Encoding of Unification in \mathcal{EL}

In the literature several methods have hitherto been used to show that an equational theory has unification type zero. These methods depend on conditions which are candidates for alternative characterizations of unification type zero. In this paper we consider the logical connection between these conditions on the abstract level of partially ordered sets. Not all of them are really equivalent to type zero.

Characterizations of unification type zero

1 Motivation and outline In order to ensure a reasonable and predictable behaviour of a Description Logic (DL) system, reasoning in the DL employed by the system should at least be decidable, and preferably of low complexity. Consequently, the expressive power of the DL in question must be restricted in an appropriate way. If the imposed restrictions are too severe, however, then the important notions of the application domain can no longer be expressed. Investigating this trade-oo between the expressivity of DLs and the complexity of their inference problems has thus been one of the most important issues in DL research. This paper investigates an approach for extending the expressivity of DLs that (in many cases) guarantees that reasoning remains decidable: the fusion of DLs. In order to explain the diierence between the usual union and the fusion of DLs, let us consider a simple example. Assume that the DL D 1 is ALC, i.e., it provides for the Boolean operators u, t, : and the additional concept constructors value restriction 8r:C and existential restriction 9r:C, and that the DL D 2 provides for the Boolean operators and number restrictions (nr) and (nr). If an application requires concept constructors from both DLs for expressing its relevant concepts, then one would usually consider the union D 1 D 2 of D 1 and D 2 , which allows for the unrestricted use of all constructors. For example, the concept description C 1 := (9r:A) u (9r::A) u (1r) is a legal D 1 D 2 description. Note that this description is unsatissable, due to the interaction between constructors of D 1 and D 2. The fusion D 1 D 2 of D 1 and D 2 prevents such interactions by imposing the following restriction: one assumes that the set of all role names is partitioned into two sets, one that can be used in constructors of D 1 , and another one that can be used in constructors of D 2. Thus, the description C 1 from above is not a legal D 1 D 2 description since it uses the same role r both in the existential restrictions (which are D 1-constructors) and in the number restriction (which is a D 2-constructor). In contrast, the descriptions 1

Fusions of Description Logics.

Whereas matching in Description Logics is now relatively well-investigated, there are only very few formal results on matching under additional side conditions, though these side conditions were already present in the original paper by Borgida and McGuinness introducing matching in DLs. The present paper closes this gap for the DL and its sublanguages

Matching under Side Conditions in Description Logics

The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. It has turned out, however, that in the presence of general concept inclusion axioms (GCIs) this extension is less straightforward than thought. In fact, a number of tableau algorithms claimed to deal correctly with fuzzy DLs with GCIs have recently been shown to be incorrect. In this paper, we concentrate on fuzzy \(\mathcal {A}\mathcal {L}\mathcal {C}\), the fuzzy extension of the well-known DL \(\mathcal {A}\mathcal {L}\mathcal {C}\). We present a terminating, sound, and complete tableau algorithm for fuzzy \(\mathcal {A}\mathcal {L}\mathcal {C}\) with arbitrary continuous t-norms. Unfortunately, in the presence of GCIs, this algorithm does not yield a decision procedure for consistency of fuzzy \(\mathcal {A}\mathcal {L}\mathcal {C}\) ontologies since it uses as a sub-procedure a solvability test for a finitely represented, but possibly infinite, system of inequations over the real interval [0,1], which are built using the t-norm. In general, it is not clear whether this solvability problem is decidable for such infinite systems of inequations. This may depend on the specific t-norm used. In fact, we also show in this paper that consistency of fuzzy \(\mathcal {A}\mathcal {L}\mathcal {C}\) ontologies with GCIs is undecidable for the product t-norm. This implies, of course, that for the infinite systems of inequations produced by the tableau algorithm for fuzzy \(\mathcal {A}\mathcal {L}\mathcal {C}\) with product t-norm, solvability is in general undecidable. We also give a brief overview of recently obtained (un)decidability results for fuzzy \(\mathcal {A}\mathcal {L}\mathcal {C}\) w.r.t. other t-norms.

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Franz Baader

Papers

SAT Encoding of Unification in \mathcal{EL}

Characterizations of unification type zero

Fusions of Description Logics.

Matching under Side Conditions in Description Logics

On the decidability status of fuzzy ALC with general concept inclusions