Matthias Knorr

Local closed world reasoning with description logics under the well-founded semantics

An important question for the upcoming Semantic Web is how to best combine open world ontology languages, such as the OWL-based ones, with closed world rule-based languages. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases (Motik and Rosati, 2010 [52]), and it is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. In this paper we propose a well-founded semantics for nondisjunctive hybrid MKNF knowledge bases that promises to provide better efficiency of reasoning, and that is compatible with both the OWL-based semantics and the traditional Well-Founded Semantics for logic programs. Moreover, our proposal allows for the detection of inconsistencies, possibly occurring in tightly integrated ontology axioms and rules, with only little additional effort. We also identify tractable fragments of the resulting language.

A Coherent Well-founded Model for Hybrid MKNF Knowledge Bases

With the advent of the Semantic Web, the question becomes important how to best combine open-world based ontology languages, like OWL, with closed-world rules paradigms. One of the most mature proposals for this combination is known as Hybrid MKNF knowledge bases [11], which is based on an adaptation of the stable model semantics to knowledge bases consisting of ontology axioms and rules. In this paper, we propose a well-founded semantics for such knowledge bases which promises to provide better efficiency of reasoning, which is compatible both with the OWL-based semantics and the traditional well-founded semantics for logic programs, and which surpasses previous proposals for such a well-founded semantics by avoiding some issues related to inconsistency handling.

Queries to Hybrid MKNF Knowledge Bases through Oracular Tabling

An important issue for the Semantic Web is how to combine open-world ontology languages with closed-world (non-monotonic) rule paradigms. Several proposals for hybrid languages allow concepts to be simultaneously defined by an ontology and rules, where rules may refer to concepts in the ontology and the ontology may also refer to predicates defined by the rules. Hybrid MKNF knowledge bases are one such proposal, for which both a stable and a well-founded semantics have been defined. The definition of Hybrid MKNF knowledge bases is parametric on the ontology language, in the sense that non-monotonic rules can extend any decidable ontology language. In this paper we define a query-driven procedure for Hybrid MKNF knowledge bases that is sound with respect to the original stable model-based semantics, and is correct with respect to the well-founded semantics. This procedure is able to answer conjunctive queries, and is parametric on an inference engine for reasoning in the on- tology language. Our procedure is based on an extension of a tabled rule evaluation to capture reasoning within an ontology by modeling it as an interaction with an external oracle and, with some assumptions on the complexity of the oracle compared to the complexity of the ontology language, maintains the data complexity of the well-founded semantics for hybrid MKNF knowledge bases.

Query-Driven Procedures for Hybrid MKNF Knowledge Bases

Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of open-world ontology languages with closed-world (nonmonotonic) rule paradigms. Based on the logic of minimal knowledge and negation as failure (MKNF), the definition of Hybrid MKNF is parametric on the description logic (DL) underlying the ontology language, in the sense that nonmonotonic rules can extend any decidable DL language. Two related semantics have been defined for Hybrid MKNF: one that is based on the Stable Model Semantics for logic programs and one on the Well-Founded Semantics (WFS). Under WFS, the definition of Hybrid MKNF relies on a bottom-up computation that has polynomial data complexity whenever the DL language is tractable. Here we define a general query-driven procedure for Hybrid MKNF that is sound with respect to the stable model-based semantics, and sound and complete with respect to its WFS variant. This procedure is able to answer a slightly restricted form of conjunctive queries, and is based on tabled rule evaluation extended with an external oracle that captures reasoning within the ontology. Such an (abstract) oracle receives as input a query along with knowledge already derived, and replies with a (possibly empty) set of atoms, defined in the rules, whose truth would suffice to prove the initial query. With appropriate assumptions on the complexity of the abstract oracle, the general procedure maintains the data complexity of the WFS for Hybrid MKNF knowledge bases. To illustrate this approach, we provide a concrete oracle for EL+, a fragment of the lightweight DL EL++. Such an oracle has practical use, as EL++ is the language underlying OWL 2 EL, which is part of the W3C recommendations for the Semantic Web, and is tractable for reasoning tasks such as subsumption. We show that query-driven Hybrid MKNF preserves polynomial data complexity when using the EL+ oracle and WFS.

Evolving Bridge Rules in Evolving Multi-Context Systems

In open environments, agents need to reason with knowledge from various sources, represented in different languages. Managed Multi-Context Systems (mMCSs) allow for the integration of knowledge from different heterogeneous sources in an effective and modular way, where so-called bridge rules express how information flows between the contexts. The problem is that mMCSs are essentially static as they were not designed to run in a dynamic scenario. Some recent approaches, among them evolving Multi-Context Systems (eMCSs), extend mMCSs by allowing not only the ability to integrate knowledge represented in heterogeneous KR formalisms, but at the same time to both react to, and reason in the presence of commonly temporary dynamic observations, and evolve by incorporating new knowledge. These approaches, however, only consider the dynamics of the knowledge bases, whereas the dynamics of the bridge rules, i.e., the dynamics of how the information flows, is neglected. In this paper, we fill this gap by building upon the framework of eMCSs by further extending it with the ability to update the bridge rules of each context taking into account an incoming stream of observed bridge rules. We show that several desirable properties are satisfied in our framework, and that the important problem of consistency management can be dealt with in our framework.

MKNF Knowledge Bases in Multi-Context Systems

In this paper we investigate the relationship between Multi-Context Systems and Hybrid MKNF Knowledge Bases. Multi-Context Systems provide an effective and modular way to integrate knowledge from different heterogeneous sources (contexts) through so-called bridge rules. Hybrid MKNF Knowledge Bases, based on the logic of minimal knowledge and negation as failure (MKNF), allow for a seamless combination of description logic ontology languages with non-monotonic logic programming rules. In this paper, we not only show that Hybrid MKNF Knowledge Bases can be used as particular contexts in Multi-Context Systems, but we also provide transformations from the former into the latter, without the need for an explicit Hybrid MKNF context, hence providing a way for agents to reason with Hybrid MKNF Knowledge Bases within Multi-Context Systems without the need for specialized Hybrid MKNF reasoners.

Forgetting under the Well-Founded Semantics

In this paper, we develop a notion of forgetting for normal logic programs under the well-founded semantics. We show that a number of desirable properties are satisfied by our approach. Three different algorithms are presented that maintain the computational complexity of the well-founded semantics, while partly keeping its syntactical structure.

Recent advances in integrating OWL and rules (technical communication)

As part of the quest for a unifyinglogic for the Semantic Web Technology Stack, a central issue is finding suitable ways of integrating description logics based on theWeb Ontology Language (OWL) with rule-based approaches based on logic programming. Such integration is difficult since naive approaches typically result in the violation of one ormore desirable design principles. For example, while both OWL 2 DL and RIF Core (a dialect of the Rule Interchange Format RIF) are decidable, their naive union is not, unless carefully chosen syntactic restrictions are applied. We report on recent advances and ongoing work by the authors in integrating OWL and rules. We take an OWL-centric perspective, which means that we take OWL 2 DL as a starting point and pursue the question of how features of rule-based formalisms can be added without jeopardizing decidability. We also report on incorporating the closed world assumption and on reasoning algorithms. This paper essentially serves as an entry point to the original papers, to which we will refer throughout, where detailed expositions of the results can be found.

Next Step for NoHR: OWL 2 QL

The Protege plug-in NoHR allows the user to combine an OWL 2 EL ontology with a set of non-monotonic logic programming rules --- suitable, e.g., to express defaults and exceptions --- and query the combined knowledge base KB. The formal approach realized in NoHR is polynomial w.r.t. data complexity and it has been shown that even very large health care ontologies, such as SNOMED CT, can be handled. As each of the tractable OWL profiles is motivated by different application cases, extending the tool to the other profiles is of particular interest, also because these preserve the polynomial data complexity of the combined formalism. Yet, a straightforward adaptation of the existing approach to OWL 2 QL turns out to not be viable. In this paper, we provide the non-trivial solution for the extension of NoHR to OWL 2 QL by directly translating the ontology into rules without any prior classification. We have implemented our approach and our evaluation shows encouraging results.

Querying OWL 2 QL and non-monotonic rules

Answering (conjunctive) queries is an important reasoning task in Description Logics (DL), hence also in highly expressive ontology languages, such as OWL. Extending such ontology languages with rules, such as those expressible in RIF-Core, and further with nonmonotonic rules, integrating default negation as described in the RIF-FLD, yields an even more expressive language that allows for modeling defaults, exceptions, and integrity constraints. Here, we present a top-down procedure for querying knowledge bases (KB) that combine non-monotonic rules with an ontology in DL-LiteR - the DL underlying the OWL 2 profile OWL 2 QL. This profile aims particularly at answering queries in an efficient way for KB with large ABoxes. Our procedure extends the query-answering facility to KB that also include non-monotonic rules, while maintaining tractability of reasoning (w.r.t. data complexity). We show that the answers are sound and complete w.r.t. the well-founded MKNF model for hybrid MKNF KB K.