A Refinement Operator for Description Logics

Description logics (DLs) and rule-based systems are two prominent families of knowledge representation formalisms. While DLs are focused on describing and reasoning about conceptual knowledge, rules are focused on answering queries about facts in the knowledge base. So far, research on DLs has been largely isolated from the research on rules. With the advent of the Semantic Web, however, it became apparent that neither formalism alone can cover all the practical use cases. The integration between DLs and rules, however, is technically challenging due to significant differences in the underlying semantic assumptions. In particular, DLs are based on standard first-order semantics and open-world assumption, whereas rules typically employ closed-world semantics based on a variant of circumscription. In my talk, I shall present an overview of the benefits of integrating DLs and rules in a coherent semantic framework, and shall discuss the main challenges in achieving a tight integration. I shall present an overview of the approaches currently discussed in literature. Finally, I shall present in more detail the approach that is based on the nonmonotonic logic MKNF by Lifschitz. This approach is tight in the sense that DLs and rules are given a common model-theoretic semantics. Furthermore, it is faithful in the sense that it is compatible with the original semantics of both DLs and rules. Finally, it is expressive and can naturally capture many of the existing proposals. I shall discuss the definitions of the semantics of the hybrid formalism, present a decision procedure for a particular decidable fragment, and discuss the complexity bounds of reasoning.

In this chapter, we show how formal knowledge representation and reasoning techniques can be used for the retrieval and interpretation of multimedia data. This section explains what we mean by an “interpretation” using examples of audio and video interpretation. Intuitively, interpretations are descriptions of media data at a high abstraction level, exposing interrelations and coherencies. In Section 3.2.3, we introduce description logics (DLs) as the formal basis for ontology languages of the OWL (web ontology language) family and for the interpretation framework described in subsequent sections. As a concrete example, we consider the interpretation of images describing a sports event in Section 3.3. It is shown that interpretations can be obtained by abductive reasoning, and a general interpretation framework is presented. Stepwise construction of an interpretation can be viewed as navigation in the compositional and taxonomical hierarchies spanned by a conceptual knowledge base. What do we mean by “interpretation” of media objects? Consider the image shown in Fig. 3.1. One can think of the image as a set of primitive objects such as persons, garbage containers, a garbage truck, a bicycle, traffic signs, trees, etc. An interpretation of the image is a description which “makes sense” of these primitive objects. In our example, the interpretation could include the assertions “two workers empty garbage containers into a garbage truck” and “a mailman distributes mail” expressed in some knowledge representation language. When including the figure caption into the interpretation process, we have a multimodal interpretation task which in this case involves visual and textual media objects. The result could be a refinement of the assertions above in terms of the location “in Hamburg”. Note that the interpretation describes activities extending in time although it is only based on a snapshot. Interpretations may generally include

This paper presents TRIPLE, a layered and modular rule language for the Semantic Web [1]. TRIPLE is based on Horn logic and borrows many basic features from F-Logic [11] but is especially designed for querying and transforming RDF models [20].TRIPLE can be viewed as a successor of SiLRI (Simple Logic-based RDF Interpreter [5]). One of the most important differences to F-Logic and SiLRI is that TRIPLE does not have a fixed semantics for object-oriented features like classes and inheritance. Its layered architecture allows such features to be easily defined for different object-oriented and other data models like UML, Topic Maps, or RDF Schema [19]. Description logics extensions of RDF (Schema) like OIL [17] and DAML+OIL [3] that cannot be fully handled by Horn logic are provided as modules that interact with a description logic classifier, e.g. FaCT [9], resulting in a hybrid rule language. This paper sketches syntax and semantics of TRIPLE.

Horn formulae are widely used in different settings that include logic programming, answer set programming, description logics, deductive databases, and system verification, among many others. One concrete example is concept subsumption in lightweight description logics, which can be reduced to inference in propositional Horn formulae. Some problems require one to reason with inconsistent Horn formulae. This is the case when providing minimal explanations of inconsistency. This paper proposes efficient algorithms for a number of decision, function and enumeration problems related with inconsistent Horn formulae. Concretely, the paper develops efficient algorithms for finding and enumerating minimal unsatisfiable subsets (MUSes), minimal correction subsets (MCSes), but also for computing the lean kernel. The paper also shows the practical importance of some of the proposed algorithms.

We tackle the problem of statistical learning in the standard knowledge base representations for the Semantic Web which are ultimately expressed in description Logics. Specifically, in our method a kernel functions for the \(\mathcal{ALCN}\) logic integrates with a support vector machine which enables the usage of statistical learning with reference representations. Experiments where performed in which kernel classification is applied to the tasks of resource retrieval and query answering on OWL ontologies.

Description Logics (DLs) denote a family of knowledge representation formalisms that allow to represent the terminological knowledge of an application domain in a structured and well-defined way. On the one hand, the name Description Logics emphasizes that the basic elements of these logics are concept descriptions, i.e., expressions that are built from concept names (unary predicates) and role names (binary predicates) using the concept constructors provided by the DL. On the other hand, unlike some of their predecessor formalisms, DLs are equipped with a formal logic-based semantics, which is usually defined in a model-theoretic way; for some DLs it can also be declared by translating concept descriptions into first-order formulae.KeywordsDescription LogicExpressive PowerInference AlgorithmInference ProblemConcept DescriptionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

There is a fundamental trade-off between the expressiveness of the language and the tractability of the reasoning task in knowledge representation. On the one hand it is widely acknowledged that relations and more generally, the expressiveness of first-order logic is extremely useful for capturing concepts required for common-sense reasoning. But at the same time the entailment problem is only semi-decidable. There have been a wide range of approaches to deal with this trade-off, from restricting the language to propositional logic to limit the expressiveness of the language in terms of the arity of the predicates (as in description logics) or the use of negation (as in Horn logic) to limit reasoning by weakening the entailment relation using non-standard semantics. In this work, we address a gap in this literature. We show that there is an intuitive fragment of first-order disjunctive knowledge, for which reasoning is decidable and can be reduced to propositional satisfiability. Knowledge bases in this fragment correspond to universally quantified first-order clauses, but without arity restrictions and without restrictions on the appearance of negation. Queries, however, are expected to be ground formulas. We achieve this result by showing how the entailment over infinitely many infinite-sized structures can be reduced to a search over finitely many finite-size structures. The crux of the argument lies in showing that constants not mentioned in the knowledge base and/or query behave identically (in a suitable formal sense). We then go on to also show that there is also an extension to this result for function symbols.

Nominalschema is an expressive description logic (DL) construct that was proposed in recent efforts to integrate DLs and (logic programming) rule-based paradigms for the Semantic Web [1] represented by two diverging W3C standards: the DL-based Web Ontology Language (OWL) [2] whose major variant, OWL 2 DL, is based on the description logic (DL) ${\mathcal{SROIQ}}$ [3]; and the rulebased Rule Interchange Format (RIF) whose core variant, called RIF Core [4], is essentially Datalog, i.e., function-free Horn logic.

This paper proposes a framework for building product information model (PIM) and product rule model (PRM), and integrated reasoning based on Description Frame Logic (DFL) [1] for collaborative product engineering environments. Most of the previous research has focused either on building ontology for PIM or on building a rule base for PRM respectively, not on both of them. Some research on product engineering has tried to build both ontology language and rule-language. But, the research is/has been limited to using both languages in a homogeneous approach under open world assumption (OWA) such as Web Ontology Language (OWL)/Semantic Web Rule Language (SWRL), which has some drawbacks to accommodate the requirements of enhanced expressivity for collaborative product engineering. We adopt Description Frame Logic (DFL) framework to integrate product semantics in PIM and engineering-specific knowledge in PRM based on description logic (DL) and logic programming (LP) under both open world assumption (OWA) and closed world assumption (CWA). This enables to secure seamless and interactive reasoning between PIM and PRM. We also include rule-expressions and constraint checking with DL for PIM while we include DL-expression in rules and LP’s non-logical features for PRM. This provides enhancement of expressiveness required for product engineering. Additionally, we show the benefits of the proposed framework with a case study.


 
 
 Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in Deviational Syntactic Structures under the label ‘EFA(X)3’ (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article—based on our OccL-based definitions of the concepts of strong implication and occurrence value as well as of the logical concept Identical Occurrence Constructor (IDOC) that is the most fundamental logical concept in our formalism—we will model Occurrence Description Logic (ODL). Accordingly, we will formally-logically analyse ‘occurrence(s) of symbol(s)’ within descriptions of the world in ODL. In addition, we will analyse and assess the logical concepts of occurrence and occurrence priority in ODL. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic.
 
 

Using mappings between ontologies is a common way of approaching the semantic heterogeneity problem on the Semantic Web. To fit into the landscape of Semantic Web languages, a suitable logic-based representation formalism for mappings is needed, which allows to reason with ontologies and mappings in an integrated manner, and to deal with uncertainty and inconsistencies in automatically created mappings. We analyze the requirements for such a formalism, and propose to use frameworks that integrate description logic ontologies with probabilistic rules. We compare two such frameworks and show the advantages of using the probabilistic extensions of their deterministic counterparts. The two frameworks that we compare are tightly coupled probabilistic dl-programs, which tightly combine the description logics behind OWL DL resp. OWL Lite, disjunctive logic programs under the answer set semantics, and Bayesian probabilities, on the one hand, and generalized Bayesian dl-programs, which tightly combine the DLP-fragment of OWL Lite with Datalog (without negation and equality) based on the semantics of Bayesian networks, on the other hand.KeywordsRepresenting probabilistic ontology mappingsrule languagesSemantic Webuncertaintyinconsistencyprobabilistic description logic programsdescription logicsdisjunctive logic programsanswer set semanticsBayesian probabilitiesBayesian description logic programsDatalogBayesian networks

We present the Angerona framework for the implementation of knowledge-based agents with a strong focus on flexibility, extensibility, and compatibility with diverse knowledge representation formalisms. As the basis for this framework we propose and formalize a general concept of compound agents in which we consider agents to consist of hierarchies of interacting epistemic and functional components. Each epistemic component is instantiated by a knowledge representation formalism. Different knowledge representation formalisms can be used within one agent and different agents in the same system can be based on different agent architectures and can use different knowledge representation formalisms. Partially instantiations define sub-frameworks for, e. g., the development of BDI agents and variants thereof. The Angerona framework realizes this concept by means of a flexible JAVA plug-in architecture for the epistemic and the functional components of an agent. The epistemic plug-ins are based on the Tweety library for knowledge representation, which provides various ready-for-use implementations and knowledge representation formalisms and a framework for the implementation of additional ones. Angerona already contains several partial and complete instantiations that implement several approaches. Angerona also features an environment plug-in for communicating agents and a flexible GUI to monitor the multiagent system and the inner workings of the agents, particularly the inspection of the dynamics of their epistemic states. Angerona and Tweety are ready to use, well documented, and open source.KeywordsKnowledge RepresentationMultiagent SystemEpistemic StateBelief BaseBelief ChangeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

There are different approaches to modeling a computational system, each providing different semantics. We present a comparison among different approaches to semantics and we aim at identifying which peculiarities are needed to provide a system with uniquely interpretable semantics. We discuss different approaches, namely, Description Logics, Artificial Neural Networks, and relational database management systems. We identify classification (the process of building a taxonomy) as common trait. However, in this chapter we also argue that classification is not enough to provide a system with a Semantics, which emerges only when relations among classes are established and used among instances. Our contribution also analyses additional features of the formalisms that distinguish the approaches: closed versus. open world assumption, dynamic versus. static nature of knowledge, the management of knowledge, and the learning process.

A real world of objects (individuals) is represented by a set of assertions written with respect to defined syntax and semantics of description logic (formal language). These assertions should be consistent with the ontology axioms described as terminology of knowledge. The axioms and the assertions represent ontology about a particular domain. A real world is a possible world if all the assertions and the axioms over its set of individuals, are consistent. It is possible then to query the possible world by specific assertions (as instance checking) to determine if they are consistent with it or not. However, ontology can contain vague concepts which means the knowledge about them is imprecise and then query answering will not possible due to the open world assumption if the necessary information is incomplete (it is currently absent). A concept description can be very exact (crisp concept) or exact (fuzzy concept) if its knowledge is complete, otherwise it is inexact (vague concept) if its knowledge is incomplete. In this paper we propose a vagueness theory based on the definition of truth gaps as ontology assertions to express the vague concepts in Ontology Web Language (OWL2) (which is based on the description logic SROIQ(D)) and an extension of the Tableau algorithm for reasoning over imprecise ontologies.

In Ontology-Based Data Access (OBDA), user queries are evaluated over a set of facts under the open world assumption, while taking into account background knowledge given in the form of a Description Logic (DL) ontology. Motivated by situation awareness applications, temporal conjunctive queries (TCQs) have recently been proposed as a useful extension of traditional OBDA to support the processing of temporal information. This paper extends the existing complexity analysis of TCQ entailment to very expressive DLs underlying the OWL 2 standard, and in contrast to previous work also allows for queries containing transitive roles.