Showing papers presented at "Web Reasoning and Rule Systems in 2009"

A Minimal Deductive System for General Fuzzy RDF

Abstract: It is well-known that crisp RDF is not suitable to represent vague information. Fuzzy RDF variants are emerging to overcome this limitations. In this work we provide, under a very general semantics, a deductive system for a salient fragment of fuzzy RDF. We then also show how we may compute the top-k answers of the union of conjunctive queries in which answers may be scored by means of a scoring function.

Paraconsistent Reasoning for OWL 2

Abstract: A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basic description logic $\mathcal{ALC}$. In this paper, we further study how to extend the four-valued semantics to the more expressive description logic $\mathcal{SROIQ}$ which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapted to tractable description logics including $\mathcal{EL++}$, DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for $\mathcal{ALC}$ and show that we can retain most of the desired properties.

An Efficient Method for Computing Alignment Diagnoses

Abstract: Formal, logic-based semantics have long been neglected in ontology matching. As a result, almost all matching systems produce incoherent alignments of ontologies. In this paper we propose a new method for repairing such incoherent alignments that extends previous work on this subject. We describe our approach within the theory of diagnosis and introduce the notion of a local optimal diagnosis. We argue that computing a local optimal diagnosis is a reasonable choice for resolving alignment incoherence and suggest an efficient algorithm. This algorithm partially exploits incomplete reasoning techniques to increase runtime performance. Nevertheless, the completeness and optimality of the solution is still preserved. Finally, we test our approach in an experimental study and discuss results with respect to runtime and diagnostic quality.

Uncertainty Reasoning for the Semantic Web

Abstract: Significant research activities have recently been directed towards the Semantic Web as a potential future substitute of the current World Wide Web. Many experts predict that the next huge step forward in Web information technology will be achieved by adding semantics to Web data. An important role in research towards the Semantic Web is played by formalisms and technologies for handling uncertainty and/or vagueness. In this paper, I first provide some motivating examples for handling uncertainty and/or vagueness in the Semantic Web. I then give an overview of some own recent formalisms for handling uncertainty and/or vagueness in the Semantic Web.

Integrating Logic Programming and Production Systems in Abductive Logic Programming Agents

Abstract: In this paper we argue the case for integrating the distinctive functionalities of logic programs and production systems within an abductive logic programming agent framework. In this framework, logic programs function as an agent's beliefs and production rules function as the agent's goals. The semantics and proof procedures are based on abductive logic programming, in which logic programs are integrated with integrity constraints that behave like production rules. Similarly to production systems, the proof procedure is an operational semantics, which manipulates the current state of a database, which is modified by actions implemented by destructive assignment. The semantics can be viewed as generating a model, based on the sequence of database states and logic program, which makes the production rules true.

Distributed Resolution for Expressive Ontology Networks

Abstract: The Semantic Web is commonly perceived as a web of partially interlinked machine readable data. This data is inherently distributed and resembles the structure of the web in terms of resources being provided by different parties at different physical locations. A number of infrastructures for storing and querying distributed semantic web data, primarily encoded in RDF have been developed but almost all the work on description logic reasoning as a basis for implementing inference in the Web Ontology Language OWL still assumes a centralized approach where the complete terminology has to be present on a single system and all inference steps are carried out on this system. We propose a distributed reasoning method that preserves soundness and completeness of reasoning under the original OWL import semantics. The method is based on resolution methods for $\mathcal{ALCHIQ}$ ontologies that we modify to work in a distributed setting. Results show a promising runtime decrease compared to centralized reasoning and indicate that benefits from parallel computation trade off the overhead caused by communication between the local reasoners.

A Preferential Tableaux Calculus for Circumscriptive ${\mathcal ALCO}$

Abstract: Nonmonotonic extensions of description logics (DLs) allow for default and local closed-world reasoning and are an acknowledged desired feature for applications, e.g. in the Semantic Web. A recent approach to such an extension is based on McCarthy's circumscription, which rests on the principle of minimising the extension of selected predicates to close off dedicated parts of a domain model. While decidability and complexity results have been established in the literature, no practical algorithmisation for circumscriptive DLs has been proposed so far. In this paper, we present a tableaux calculus that can be used as a decision procedure for concept satisfiability with respect to concept-circumscribed ${\mathcal ALCO}$ knowledge bases. The calculus builds on existing tableaux for classical DLs, extended by the notion of a preference clash to detect the non-minimality of constructed models.

A Hybrid Architecture for a Preoperative Decision Support System Using a Rule Engine and a Reasoner on a Clinical Ontology

Abstract: We report on a preventive care software system for preoperative risk assessment of patient undergoing elective surgery. The system combines a rule engine and a reasoner which uses a decision support ontology developed with a logic based knowledge representation formalism. We specifically discuss our experience of using a representation of a patient's medical history in OWL, combined with a reasoning tool to suggest appropriate preoperative tests based on an implementation of preoperative assessment guidelines. We illustrate the reasoning functionalities of the system with a number of practical examples.

On the Ostensibly Silent `W' in OWL 2 RL

Abstract: In this paper, we discuss the draft OWL 2 RL profile from the perspective of applying the constituent rules over Web data. In particular, borrowing from previous work, we discuss (i) optimisations based on a separation of terminological data from assertional data and (ii) the application of authoritative analysis to constrain third party interference with popular ontology terms. We also provide discussion relating to the applicability of new OWL 2 constructs for two popular Semantic Web ontologies --- namely FOAF and SIOC --- and provide some evaluation of the proposed use-cases based on reasoning over a representative Web dataset of approx. 12 million statements.

Answer Sets in a Fuzzy Equilibrium Logic

Abstract: Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications. As one of the most general "classical" approaches, answer sets of arbitrary propositional theories can be defined as models in the equilibrium logic of Pearce. Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems. In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic. We show that the resulting notion of answer set is compatible with existing definitions, when the syntactic restrictions of the corresponding approaches are met. We furthermore locate the complexity of the main reasoning tasks at the second level of the polynomial hierarchy. Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.

A Logic Based Approach to the Static Analysis of Production Systems

Abstract: In this paper we present an embedding of propositional production systems into μ -calculus, and first-order production systems into fixed-point logic, with the aim of using these logics for the static analysis of production systems with varying working memories. We encode properties such as termination and confluence in these logics, and briefly discuss which ones cannot be expressed, depending on the expressivity of the logic. We show how the embeddings can be used for reasoning over the production system, and use known results to obtain upper bounds for special cases. The strong correspondence between the structure of the models of the encodings and the runs of the production systems enables the straightforward modeling of properties of the system in the logic.

A Formal Theory for Modular ERDF Ontologies

Abstract: The success of the Semantic Web is impossible without any form of modularity, encapsulation, and access control. In an earlier paper, we extended RDF graphs with weak and strong negation, as well as derivation rules. The ERDF #n -stable model semantics of the extended RDF framework (ERDF ) is defined, extending RDF(S) semantics. In this paper, we propose a framework for modular ERDF ontologies, called modular ERDF framework , which enables collaborative reasoning over a set of ERDF ontologies, while support for hidden knowledge is also provided. In particular, the modular ERDF stable model semantics of modular ERDF ontologies is defined, extending the ERDF #n -stable model semantics. Our proposed framework supports local semantics and different points of view, local closed-world and open-world assumptions, and scoped negation-as-failure. Several complexity results are provided.

The Perfect Match: RPL and RDF Rule Languages

Abstract: Path query languages have been previously shown to complement RDF rule languages in a natural way and have been used as a means to implement the RDFS derivation rules. RPL is a novel path query language specifically designed to be incorporated with RDF rules and comes in three flavors: Node -, edge - and path -flavored expressions allow to express conditional regular expressions over the nodes, edges, or nodes and edges appearing on paths within RDF graphs. Providing regular string expressions and negation, RPL is more expressive than other RDF path languages that have been proposed. We give a compositional semantics for RPL and show that it can be evaluated efficiently, while several possible extensions of it cannot.

Scalable Web Reasoning Using Logic Programming Techniques

Abstract: One of the key issues for the uptake of the Semantic Web idea is the availability of reasoning techniques that are usable on a large scale and that offer rich modelling capabilities by providing comprehensive coverage of the OWL language. In this paper we present a scalable extension of our ABox reasoning framework called DLog. DLog performs query-driven execution whereby the terminological part of the description logic knowledge base is converted into a Logic Program and the assertional facts are accessed dynamically from a database. The problem of instance retrieval is reduced to a series of instance checks over a set of individuals containing all solutions for the query. Such a superset is calculated by using static-code analysis on the generated program. We identify two kinds of parallelism within DLog execution: (1) the instances in the superset can be independently checked in parallel and (2) a specific instance check can be executed in parallel by specialising well-established techniques from Logic Programming. Moreover, for efficiency reasons, we propose to use a specialised abstract machine rather than relying on the more generic WAM execution model. We describe the architecture of a distributed framework in which the above mentioned techniques are integrated. We compare our results to existing approaches.

SILK: Higher Level Rules with Defaults and Semantic Scalability

Abstract: We overview the technical approach and motivations of the SILK system for semantic rules and ontologies, that radically extends the knowledge representation (KR) power of currently commercially important business rule systems, including not only Prologs but also production rules and event-condition-action rules, database systems, and semantic web.

Belief Logic Programming with Cyclic Dependencies

Abstract: Our previous work [26] introduced Belief Logic Programming (BLP), a novel form of quantitative logic programming with correlation of evidence. Unlike other quantitative approaches to logic programming, this new theory is able to provide accurate conclusions in the presence of uncertainty when the sources of information are not independent. However, the semantics defined in [26] is not sufficiently general--it does not allow cyclic dependencies among beliefs, which is a serious limitation of expressive power. This paper extends the semantics of BLP to allow cyclic dependencies. We show that the new semantics is backward compatible with the semantics for acyclic BLP and has the expected properties. The results are illustrated with examples of inference in a simple diagnostic expert system.

A Reasoner for Simple Conceptual Logic Programs

Abstract: Open Answer Set Programming (OASP) can be seen as a framework to represent tightly integrated combined knowledge bases of ontologies and rules that are not necessarily DL-safe The framework makes the open-domain assumption and has a rule-based syntax supporting negation under a stable model semantics Although decidability of different fragments of OASP has been identified, reasoning and effective algorithms remained largely unexplored In this paper, we describe an algorithm for satisfiability checking of the fragment of simple Conceptual Logic Programs and provide a BProlog implementation To the best of our knowledge, this is the first implementation of a (fragment) of a framework that can tightly integrate ontologies and non-DL-safe rules under an expressive nonmonotonic semantics

Search for More Declarativity

Abstract: Good tree search algorithms are a key requirement for inference engines of rule languages. As Prolog exemplifies, inference engines based on traditional uninformed search methods with their well-known deficiencies are prone to compromise declarativity, the primary concern of rule languages. The paper presents a new family of uninformed search algorithms that combine the advantages of the traditional ones while avoiding their shortcomings. Moreover, the paper introduces a formal framework based on partial orderings, which allows precise and elegant analysis of such algorithms.

An Exact algorithm to minimize the makespan in project scheduling with scarce resources and feeding precedence relations

Abstract: In this paper we study an extension of the Resource-Constrained Project Scheduling Problem (RCPSP) with minimum makespan objective by introducing as precedence constraints the so called “Feeding Precedences” (FP). For the RCPSP with FP we propose a new mathematical formulation and a branch and bound algorithm exploiting the latter formulation. The exact algorithm takes advantage also of a lower bound based on a Lagrangian relaxation of the same formulation. A computational experimentation on randomly generated instances and a comparison with the results achieved by a commercial solver, show that the proposed approach is able to behave satisfactorily.