In Description Logics the reasoning service most specific concept (msc) constructs a concept description that generalizes an ABox individual into a concept description. For the Description Logic EL the msc may not exist, if computed with respect to general EL-TBoxes or cyclic ABoxes. However, it is still possible to find a concept description that is the msc up to a fixed role-depth, i.e. with respect to a maximal nesting of quantifiers. In this report we present a practical approach for computing the roledepth bounded msc, based on the polynomial-time completion algorithm for EL. We extend these methods to Prob-EL⁰¹c , which is a probabilistic variant of EL. Together with the companion report [9] this report devises computation methods for the bottom-up construction of knowledge bases for EL and Prob-EL⁰¹c .

The Description Logic EL is an inexpressive knowledge representation language, which nevertheless has recently drawn considerable attention in the knowledge representation and the ontology community since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. 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 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 problem in 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 solverswhen implementing an EL-unification algorithm. On the other hand, this reduction provides us with a proof of the fact that EL-unification is in NP that is much simpler than the one given in our previous paper on EL-unification.

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, EL allows the use of the top concept (>), which represents the whole interpretation domain, whereas the large medical ontology SNOMEDCT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSpace-complete. / This is an updated version of the original report that includes Appendix A on locality of unifiers.

We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic FL₀. The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.

Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning.

In the work of Baader and Distel, a method has been proposed to axiomatize all general concept inclusions (GCIs) expressible in the description logic EL⊥ and valid in a given interpretation I. This provides us with an effective method to learn EL⊥-ontologies from interpretations, which itself can be seen as a different representation of linked data. In another report, we have extended this approach to handle errors in the data. This has been done by not only considering valid GCIs but also those whose confidence is above a certain threshold 𝑐. In the present work, we shall extend the results by describing another way to compute bases of confident GCIs. We furthermore provide experimental evidence that this approach can be useful for practical applications. We finally show that the technique of unravelling can also be used to effectively turn confident EL⊥gfp-bases into EL⊥-bases.

Removing unwanted consequences from a knowledge base has been investigated in belief change under the name contraction and is called repair in ontology engineering. Simple repair and contraction approaches based on removing statements from the knowledge base (respectively called belief base contractions and classical repairs) have the disadvantage that they are syntax-dependent and may remove more consequences than necessary. Belief set contractions do not have these problems, but may result in belief sets that have no finite representation if one works with logics that are not fragments of propositional logic. Similarly, optimal repairs, which are syntax-independent and maximize the retained consequences, may not exist. In this paper, we want to leverage advances in characterizing and computing optimal repairs of ontologies based on the description logics EL to obtain contraction operations that combine the advantages of belief set and belief base contractions. The basic idea is to employ, in the partial meet contraction approach, optimal repairs instead of optimal classical repairs as remainders. We introduce this new approach in a very general setting, and prove a characterization theorem that relates the obtained contractions with well-known postulates. Then, we consider several interesting instances, not only in the standard repair/contraction setting where one wants to get rid of a consequence, but also in other settings such as variants of forgetting in propositional and description logic. This is an extended version of an article accepted at KR 2024.

A combinação de lógica e probabilidade (lógicas probabilísticas) tem sido um tópico bastante estudado nas últimas décadas. A maioria de propostas para estes formalismos pressupõem que tanto as sentenças lógicas como as probabilidades sejam especificadas por especialistas. Entretanto, a crescente disponibilidade de dados relacionais sugere o uso de técnicas de aprendizado de máquina para produzir sentenças lógicas e estimar probabilidades. Este trabalho apresenta contribuições em termos de representação de conhecimento e aprendizado. Primeiro, uma linguagem lógica probabilística de primeira ordem é proposta. Em seguida, três algoritmos de aprendizado de lógica de descrição probabilística crALC são apresentados: um algoritmo probabilístico com ênfase na indução de sentenças baseada em classificadores Noisy-OR; um algoritmo que foca na indução de inclusões probabilísticas (componente probabilístico de crALC); um algoritmo de natureza probabilística que induz sentenças lógicas ou inclusões probabilísticas. As propostas de aprendizado são avaliadas em termos de acurácia em duas tarefas: no aprendizado de lógicas de descrição e no aprendizado de terminologias probabilísticas em crALC. Adicionalmente, são discutidas aplicações destes algoritmos em processos de recuperação de informação: duas abordagens para extensão semântica de consultas na Web usando ontologias probabilísticas são discutidas. / The combination of logic and probabilities (probabilistic logics) is a topic that has been extensively explored in past decades. The majority of work in probabilistic logics assumes that both logical sentences and probabilities are specified by experts. As relational data is increasingly available, machine learning algorithms have been used to induce both logical sentences and probabilities. This work contributes in knowledge representation and learning. First, a rst-order probabilistic logic is proposed. Then, three algorithms for learning probabilistic description logic crALC are given: a probabilistic algorithm focused on learning logical sentences and based on Noisy-OR classiers; an algorithm that aims at learning probabilistic inclusions (probabilistic component of crALC) and; an algorithm that using a probabilistic setting, induces either logical sentences or probabilistic inclusions. Evaluation of these proposals has been performed in two situations: by measuring learning accuracy of both description logics and probabilistic terminologies. In addition, these learning algorithms have been applied to information retrieval processes: two approaches for semantic query extension through probabilistic ontologies are discussed.

FROTA, Débora Farias. Uma Lógica de Descrição Default. 2011. 79 f. : Dissertação (mestrado) - Universidade Federal do Ceará. Centro de Ciências, Coordenação do Programa de Pós-Graduação em Computação, Fortaleza-CE, 2011. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-06-20T19:27:19Z No. of bitstreams: 1 2011_dis_dffrota.pdf: 945021 bytes, checksum: 9adb958d87b14104dcd8db9fc4c4bd6f (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-06-20T19:28:34Z (GMT) No. of bitstreams: 1 2011_dis_dffrota.pdf: 945021 bytes, checksum: 9adb958d87b14104dcd8db9fc4c4bd6f (MD5) / Made available in DSpace on 2016-06-20T19:28:34Z (GMT). No. of bitstreams: 1 2011_dis_dffrota.pdf: 945021 bytes, checksum: 9adb958d87b14104dcd8db9fc4c4bd6f (MD5) Previous issue date: 2011 / Knowledge formalization and reasoning automatization are central within Arti cial Intelligence. First Order Logic has been traditionally used for such purposes. However, it is better suited to deal with complete knowledge in ideal circumstances. In real situations, in which the knowledge is partial, First Order Logic is not su cient. Nonmonotonic logics have been proposed to better cope with practical reasoning. A successful formalization of nonmonotonic reasoning is the Reiter's default logic which extends classical logic with default rules. Unfortunately, default logic is undecidable. In this work, we propose a description default logic expressible enough to formalize practical reasoning in knowledge bases. It has as its monotonic basis the ALC Description Logic. We add some restrictions to the application of defaults in order to obtain nice properties such as coherence and the elimination of anomalous extensions. We present the main algorithms used to build an extension with a step by step complexity analysis. / A formalização do conhecimento e a automatização do raciocínio são assuntos centrais de pesquisa da Inteligência Arti cial. A Lógica de Primeira Ordem tem sido tradicionalmente utilizada para tais propósitos. No entanto, ela é mais adequada para lidar com conhecimento completo em circunstâncias ideais. Em situações reais, nas quais o conhecimento é parcial, a Lógica de Primeira Ordem não é su ciente. Lógicas não-monotônicas têm sido propostas para melhor lidar com o raciocínio prático. Uma formalização do raciocínio não-monotônico bem-sucedida é a Lógica Default de Reiter que estende a Lógica de Primeira Ordem com regras default. Infelizmente, a Lógica Default é indecidível. Nesta dissertação, propomos uma Lógica de Descrição Default expressiva o su ciente para formalizar o raciocínio prático sobre bases de conhecimento. Ela tem como base monotônica a Lógica de Descrição ALC. Adicionamos algumas restrições à aplicação dos defaults a m de obter propriedades interessantes, tais como a coerência e a eliminação de extensões anômalas. Apresentamos os principais algoritmos usados para construir uma extensão com um passo-a-passo e suas análise de complexidade.