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Local Closed World Reasoning with Description Logics under the Well-Founded Semantics
, 2011
"... 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 [52], and it is based on an adap ..."
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Cited by 35 (26 self)
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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 [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.
OWL and rules
- In Reasoning Web, Semantic Technologies for the Web of Data - 7th International Summer School 2011
"... Abstract. The relationship between the Web Ontology Language OWL and rule-based formalisms has been the subject of many discussions and research investigations, some of them controversial. From the many at-tempts to reconcile the two paradigms, we present some of the newest developments. More precis ..."
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Cited by 21 (12 self)
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Abstract. The relationship between the Web Ontology Language OWL and rule-based formalisms has been the subject of many discussions and research investigations, some of them controversial. From the many at-tempts to reconcile the two paradigms, we present some of the newest developments. More precisely, we show which kind of rules can be mod-eled in the current version of OWL, and we show how OWL can be extended to incorporate rules. We finally give references to a large body of work on rules and OWL. 1
Implementing Query Answering for Hybrid MKNF Knowledge Bases
"... Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as ..."
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Cited by 18 (4 self)
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Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general Oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF (ALCQ) theory.
A query tool for EL with non-monotonic rules
- In Procs. of ISWC
, 2013
"... Abstract. We present the Protége ́ plug-in NoHR that allows the user to take an EL+ ⊥ ontology, add a set of non-monotonic (logic programming) rules – suitable e.g. to express defaults and exceptions – and query the combined knowledge base. Our approach uses the well-founded semantics for MKNF know ..."
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Cited by 13 (12 self)
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Abstract. We present the Protége ́ plug-in NoHR that allows the user to take an EL+ ⊥ ontology, add a set of non-monotonic (logic programming) rules – suitable e.g. to express defaults and exceptions – and query the combined knowledge base. Our approach uses the well-founded semantics for MKNF knowledge bases as underlying formalism, so no restriction other than DL-safety is imposed on the rules that can be written. The tool itself builds on the procedure SLG(O) and, with the help of OWL 2 EL reasoner ELK, pre-processes the ontology into rules, whose result together with the non-monotonic rules serve as input for the top-down querying engine XSB Prolog. With the resulting plug-in, even queries to very large ontologies, such as SNOMED CT, augmented with a large number of rules, can be processed at an interactive response time after one initial brief pre-processing period. At the same time, our system is able to deal with possible inconsistencies between the rules and an ontology that alone is consistent. 1
Local Closed World Semantics: Keep it simple, stupid!
"... Abstract. A combination of open and closed-world reasoning (usually called local closed world reasoning) is a desirable capability of knowledge representation formalisms for Semantic Web applications. However, none of the proposals made to date for extending description logics with local closed worl ..."
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Cited by 12 (5 self)
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Abstract. A combination of open and closed-world reasoning (usually called local closed world reasoning) is a desirable capability of knowledge representation formalisms for Semantic Web applications. However, none of the proposals made to date for extending description logics with local closed world capabilities has had any significant impact on applications. We believe that one of the key reasons for this is that current proposals fail to provide approaches which are intuitively accessible for application developers and at the same time are applicable, as extensions, to expressive description logics such as SROIQ, which underlies the Web Ontology Language OWL. In this paper we propose a new approach which overcomes key limitations of other major proposals made to date. It is based on an adaptation of circumscriptive description logics which, in contrast to previously reported circumscription proposals, is applicable to SROIQ without rendering reasoning over the resulting language undecidable.
Normative systems represented as hybrid knowledge bases
- In
, 2011
"... Abstract. Normative systems have been advocated as an effective tool to regulate interaction in multi-agent systems. Logic programming rules intuitively correspond to conditional norms, and their semantics is based on the closed world assumption, which allows default negation, often used in norms. H ..."
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Cited by 11 (4 self)
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Abstract. Normative systems have been advocated as an effective tool to regulate interaction in multi-agent systems. Logic programming rules intuitively correspond to conditional norms, and their semantics is based on the closed world assumption, which allows default negation, often used in norms. However, there are cases where the closed world assumption is clearly not adequate, and others that require reasoning about unknown individuals, which is not possible in logic programming. On the other hand, description logics are based on the open world assumption and support reasoning about unknown individuals, but do not support default negation. In this paper, we demonstrate the need for the aforementioned features (closed and open world assumptions, and reasoning about unknown individuals) in order to model human laws, with examples from the Portuguese Penal Code. We advocate the use of hybrid knowledge bases combining rules and ontologies, which provide the joint expressivity of logic programming and description logics. We define a normative scenario as the pair of a set of facts and a set of norms, and give it a formal semantics by translation into an MKNF knowledge base. We describe the implementation of the language, which computes the relevant consequences of given facts and norms, and use it to establish the resulting sentence in a penal scenario. 1
A Query-driven Procedures for Hybrid MKNF Knowledge Bases
"... Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of openworld ontology languages with closed-world (non-monotonic) rule paradigms. Based on the logic of minimal knowledge and negation as failure (MKNF), the definition of Hybrid MKNF is parametric on the descr ..."
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Cited by 10 (10 self)
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Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of openworld ontology languages with closed-world (non-monotonic) 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 non-monotonic 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.
Local Closed-World Reasoning with Description Logics under the Well-founded Semantics
, 2010
"... 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 rules paradigms. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases [41], which is based on an adaptation ..."
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Cited by 8 (2 self)
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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 rules paradigms. One of the most mature proposals for this combination is known as hybrid MKNF knowledge bases [41], 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 knowl-edge bases which promises to provide better efficiency of reasoning and is com-patible both with the OWL-based semantics and the traditional Well-Founded Semantics for logic programs. Moreover, our proposal permits the detection of inconsistencies possibly occuring in tightly integrated ontology axioms and rules with only little additional effort. We also identify tractable fragments of the resulting language.
Towards Closed World Reasoning in Dynamic Open Worlds
- TPLP Special Issue 10(4-6
, 2010
"... The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment ..."
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Cited by 6 (3 self)
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The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.
J.J.: Querying owl 2 ql and non-monotonic rules
, 2011
"... Abstract. 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 non-monotonic rules, integrating ..."
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Cited by 6 (6 self)
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Abstract. 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 non-monotonic rules, integrating default negation as described in the RIF-FLD, yields an even more expressive language that allows for modeling defaults, ex-ceptions, 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 rea-soning (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. 1