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Query answering over Description Logic (DL) ontologies has become a vibrant field of research. Efficient realizations often exploit database technology and rewrite a given query to an equivalent SQL or Datalog query over a database associated with the ontology. This approach has been intensively studied for conjunctive query answering in the DL-Lite and EL families, but is much less explored for more expressive DLs and queries. We present a rewriting-based algorithm for conjunctive query answering over Horn-SHIQ ontologies, possibly extended with recursive rules under limited recursion as in DL+log. This setting not only subsumes both DL-Lite and EL, but also yields an algorithm for answering (limited) recursive queries over Horn-SHIQ ontologies (an undecidable problem for full recursive queries). A prototype implementation shows its potential for applications, as experiments exhibit efficient query answering over full Horn-SHIQ ontologies and benign downscaling to DL-Lite, where it is competitive with comparable state of the art systems.

Logic programming has always been a major ontology modeling paradigm, and is frequently being used in large research projects and industrial applications, e.g., by means of the F-Logic reasoning engine OntoBroker or the TRIPLE query, inference, and transformation language and system. At the same time, the Web Ontology Language OWL has been recommended by the W3Cfor modeling ontologies for the web. Naturally, it is desirable to investigate the interoperability between both paradigms. In this paper, we do so by studying an expressive fragement of OWL DL for which reasoning can be reduced to the evaluation of Horn logic programs. Building on the KAON 2 algorithms for transforming OWL DL into disjunctive Datalog, we give a detailed account of how and to what extent OWL DL can be employed in standard logic programming systems. En route, we derive a novel, simplified characterization of the supported fragment of OWL DL. © 2006 IEEE.

Answer set programs with external source access may introduce new constants that are not present in the program, which is known as value invention. As naive value invention leads to programs with infinite grounding and answer sets, syntactic safety criteria are imposed on programs. However, traditional criteria are in many cases unnecessarily strong and limit expressiveness. We present liberal domain-expansion (de-) safe programs, a novel generic class of answer set programs with external source access that has a finite grounding and allows for value invention. De-safe programs use so-called term bounding functions as a parameter for modular instantiation with concrete—e.g., syntactic or semantic or both—safety criteria. This ensures extensibility of the approach in the future. We provide concrete instances of the framework and develop an operator that can be used for computing a finite grounding. Finally, we discuss related notions of safety from the literature, and show that our approach is strictly more expressive.

Answer Set Programming (ASP) has been deployed in many applications, thanks to the availability of efficient solvers. Most programs encountered in practice have an important property: Their predicate arities are bounded by a constant, and in this case it is known that the relevant computations can be done using polynomial space. However, all competitive ASP systems rely on grounding, due to which they may use exponential space for these programs. We present three evaluation methods that respect the polynomial space bound and a generic framework architecture for realization. Experimental results for a prototype implementation indicate that the methods are effective. They show not only benign space consumption, but interestingly also good runtime compared to some state of the art ASP solvers.

This chapter gives an extended introduction to the lightweight profiles OWL EL, OWL QL, and OWL RL of the Web Ontology Language OWL. The three ontology language standards are sublanguages of OWL DL that are restricted in ways that significantly simplify ontological reasoning. Compared to OWL DL as a whole, reasoning algorithms for the OWL profiles show higher performance, are easier to implement, and can scale to larger amounts of data. Since ontological reasoning is of great importance for designing and deploying OWL ontologies, the profiles are highly attractive for many applications. These advantages come at a price: various modelling features of OWL are not available in all or some of the OWL profiles. Moreover, the profiles are mutually incomparable in the sense that each of them offers a combination of features that is available in none of the others. This chapter provides an overview of these differences and explains why some of them are essential to retain the desired properties. To this end, we recall the relationship between OWL and description logics (DLs), and show how each of the profiles is typically treated in reasoning algorithms. © 2012 Springer-Verlag.

The purpose of this chapter is to report on work that has been done in the REWERSE project concerning hybrid reasoning with rules and ontologies. Two major streams of work have been pursued within REWERSE. They start from the predominant semantics of non-monotonic rules in logic programming. The one stream was an extension of non-monotonic logic programs under answer set semantics, with query interfaces to external knowledge sources. The other stream, in the spirit of the AL-log approach of enhanced deductive databases, was an extension of Datalog (with the well-founded semantics, which is predominant in the database area). The former stream led to so-called non-monotonic dl-programs and hex-programs, and the latter stream to hybrid well-founded semantics. Further variants and derivations of the formalisms (like a well-founded semantics for dl-programs, respecting probabilistic knowledge, priorities, etc.) have been conceived.

This survey article introduces into the essential concepts and methods underlying rule-based query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation. The treatment of these areas is foundation-oriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the “Rule Interchange Framework (RIF)” currently being developed in a working group of the W3C. Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in F-Logic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed.

Consider an agent executing a plan with nondeterministic actions, in a dynamic environment, which might fail. Suppose that she is given a description of this action domain, including specifications of effects of actions, and a set of trajectories for the execution of this plan, where each trajectory specifies a possible execution of the plan in this domain. After executing some part of the plan, suppose that she obtains information about the current state of the world, and notices that she is not at a correct state relative to the given trajectories. How can she find an explanation (a point of failure) for such a discrepancy? An answer to this question can be useful for different purposes. In the context of execution monitoring, points of failure can determine some checkpoints that specify when to check for discrepancies, and they can sometimes be used for recovering from discrepancies that cause plan failures. At the modeling level, points of failure may provide useful insight into the action domain for a better understanding of the domain, or reveal errors in the formalization of the domain. We study the question above in a general logic-based knowledge representation framework, which can accommodate nondeterminism and concurrency. In this framework, we define a discrepancy and an explanation for it, and analyze the computational complexity of detecting discrepancies and finding explanations for them. We introduce a method for computing explanations, and report about a realization of this method using DLVK, which is a logic-programming based system for reasoning about actions and change.

Towards the integration of rules and ontologies in the Semantic Web, we propose a combination of logic programming under the answer set semantics with the description logics SHIF(D) and SHOIN(D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. This combination allows for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We introduce description logic programs (dl-programs), which consist of a description logic knowledge base L and a finite set of description logic rules (dl-rules) P. Such rules are similar to usual rules in logic programs with negation as failure, but may also contain queries to L, possibly default negated, in their bodies. We define Herbrand models for dl-programs, and show that satisfiable positive dl-programs have a unique least Herbrand model. More generally, consistent stratified dl-programs can be associated with a unique minimal Herbrand model that is characterized through iterative least Herbrand models. We then generalize the (unique) minimal Herbrand model semantics for positive and stratified dl-programs to a strong answer set semantics for all dl-programs, which is based on a reduction to the least model semantics of positive dl-programs. We also define a weak answer set semantics based on a reduction to the answer sets of ordinary logic programs. Strong answer sets are weak answer sets, and both properly generalize answer sets of ordinary normal logic programs. We then give fixpoint characterizations for the (unique) minimal Herbrand model semantics of positive and stratified dl-programs, and show how to compute these models by finite fixpoint iterations. Furthermore, we give a precise picture of the complexity of deciding strong and weak answer set existence for a dl-program.

We analyze the computational complexity of Halpern and Pearl's (causal) explanations in the structural-model approach, which are based on their notions of weak and actual cause. In particular, we give a precise picture of the complexity of deciding explanations, alpha-partial explanations, and partial explanations, and of computing the explanatory power of partial explanations. Moreover, we analyze the complexity of deciding whether an explanation or an alpha-partial explanation over certain variables exists. We also analyze the complexity of deciding explanations and partial explanations in the case of succinctly represented context sets, the complexity of deciding explanations in the general case of situations, and the complexity of deciding subsumption and equivalence between causal models. All complexity results are derived for the general case, as well as for the restriction to the case of binary causal models, in which all endogenous variables may take only two values. To our knowledge, no complexity results for explanations in the structural-model approach have been derived so far. Our results give insight into the computational structure of Halpern and Pearl's explanations, and pave the way for efficient algorithms and implementations.