Giovambattista Ianni

Combining answer set programming with description logics for the Semantic Web

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 Her-brand model. More generally, consistent stratified dl-programs can be associated with a unique minimal Her-brand 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.

Effective integration of declarative rules with external evaluations for semantic-web reasoning

Towards providing a suitable tool for building the Rule Layer of the Semantic Web, hex-programs have been introduced as a special kind of logic programs featuring capabilities for higher-order reasoning, interfacing with external sources of computation, and default negation. Their semantics is based on the notion of answer sets, providing a transparent interoperability with the Ontology Layer of the Semantic Web and full declarativity. In this paper, we identify classes of hex-programs feasible for implementation yet keeping the desirable advantages of the full language. A general method for combining and evaluating sub-programs belonging to arbitrary classes is introduced, thus enlarging the variety of programs whose execution is practicable. Implementation activity on the current prototype is also reported.

Reasoning with Rules and Ontologies

For realizing the Semantic Web vision, extensive work is underway for getting the layers of its conceived architecture ready. Given that the Ontology Layer has reached a certain level of maturity with W3C recommendations such as RDF and the OWL Web Ontology Language, current interest focuses on the Rules Layer and its integration with the Ontology Layer. Several proposals have been made for solving this problem, which does not have a straightforward solution due to various obstacles. One of them is the fact that evaluation principles like the closed-world assumption, which is common in rule languages, are usually not adopted in ontologies. Furthermore, naively adding rules to ontologies raises undecidability issues. In this paper, after giving a brief overview about the current state of the Semantic-Web stack and its components, we will discuss nonmonotonic logic programs under the answer-set semantics as a possible formalism of choice for realizing the Rules Layer. We will briefly discuss open issues in combining rules and ontologies, and survey some existing proposals to facilitate reasoning with rules and ontologies. We will then focus on description-logic programs (or dl-programs, for short), which realize a transparent integration of rules and ontologies supported by existing reasoning engines, based on the answer-set semantics. We will further discuss a generalization of dl-programs, viz.hex-programs, which offer access to different ontologies as well as higher-order language constructs.

Hybrid reasoning with rules and ontologies

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 nonmonotonic 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 nonmonotonic dl-programs and HEX-programs, and the latter stream to hybrid wellfounded semantics. Further variants and derivations of the formalisms (like a well-founded semantics for dl-programs, respecting probabilistic knowledge, priorities, etc.) have been conceived.

dlvhex: A Prover for Semantic-Web Reasoning under the Answer-Set Semantics

We present the system dlvhex, a solver for HEX-programs, which are nonmonotonic logic programs admitting both higher-order atoms as well as external atoms. Higher-order features are widely acknowledged as being useful for various tasks, including meta-reasoning. Furthermore, the possibility to exchange knowledge with external sources in a fully declarative paradigm such as answer-set programming (ASP) becomes increasingly important, in particular in view of applications in the semantic-Web area. Through external atoms, HEX-programs can deal with external knowledge and reasoners of various nature, such as RDF datasets or description-logics knowledge bases

Nonmonotonic description logic programs : Implementation and experiments

The coupling of description logic reasoning systems with other reasoning formalisms (possibly over the Web) is becoming an important research issue and calls for advanced methods and algorithms. Recently, several notions of description logic programs have been introduced, combining rule-based semantics with description logics. Among them are nonmonotonic description logic programs (or dl-programs for short) which combine nonmonotonic logic programs with description logics under a generalized version of the answer-set and the well-founded semantics, respectively, which are the predominant semantics for nonmonotonic logic programs. In this paper, we consider some technical issues regarding an efficient implementation for both semantics, which has been realized in a working prototype exploiting the two state-of-art tools DLV and RACER. A major issue in this respect is efficient interfacing between the two reasoning systems at hand, for which we devised special methods. Such methods may fruitfully be used for the implementation of systems of similar nature. Reported experimentation activities with our prototype show that the methods we have developed are effective and are a key for highly optimized nonmonotonic dl-program engines.

Efficiently Querying RDF(S) Ontologies with Answer Set Programming

Ontologies are pervading many areas of knowledge representation and management. To date, most research efforts have been spent on the development of sufficiently expressive languages for the representation and querying of ontologies; however, querying efficiency has received attention only recently, especially for ontologies referring to large amounts of data. In fact, it is still uncertain how reasoning tasks will scale when applied on massive amounts of data. This work is a first step toward this setting: it first shows that Resource Description Framework(Schema) [RDF(S)] ontologies can be expressed, without loss of semantics, into Answer Set Programming (ASP). Then, based on a previous result showing that the SPARQL query language (a candidate W3C recommendation for RDF(S) ontologies) can be mapped to a rule-based language, it shows that efficient querying of big ontologies can be accomplished with a database oriented extension of the well known ASP system DLV, which we recently developed. Results reported in the article show that our proposed framework is promising for the improvement of both scalability and expressiveness of available RDF(S) storage and query systems.

The IMPL Policy Language for Managing Inconsistency in Multi-Context Systems

Multi-context systems are a declarative formalism for interlinking knowledge-based systems (contexts) that interact via (possibly nonmonotonic) bridge rules. Interlinking knowledge provides ample opportunity for unexpected inconsistencies. These are undesired and come in different categories: some may simply be repaired automatically, while others are more serious and must be inspected by a human operator. In general, no one-fits-all solution exists, since these categories depend on the application scenario. To nevertheless tackle inconsistencies in a general and principled way, we thus propose a declarative policy language for inconsistency management in multi-context systems. We define its syntax and semantics, discuss methodologies for applying the language in real world applications, and outline an implementation by rewriting to acthex, a formalism extending Answer Set Programs.