1. 1. Motivation Knowledge in the Semantic Web must be shared and modularly organised. The semantics of the modular ERDF framework has been defined model theoretically [1,2], but it was lacking a declarative rule-based semantics for implementing the system. The existing MWeb framework provides general mechanisms to specify modular rulebases in the Semantic Web, and has a working implementation supporting some of the Rule Interchange Format (RIF) constructs. Idea: use the MWeb framework to specify a rule-based semantics for interesting fragments of modular ERDF allowing for the integration of both frameworks, with an implementation. Carlos Viegas Damásio CENTRIA, FCT/UNL, Portugal Anastasia Analyti FORTH-ICS, Crete Grigoris Antoniou FORTH-ICS and Univ. Crete Implementing simple modular ERDF ontologies Provides an embedding of simple Extended Resource Description Framework ontologies into the Modular Web framework with a corresponding encoding and implementation in logic programming 4. Translations A typical simple modular ERDF ontology translated into the MWeb framework is shown below, as well as the corresponding encoding into extended logic program. The resulting extended logic program uses the 4- ary predicate '->'(r,p,s,o) to denote that triple s.[p ->> o] holds at r. 2. Simple Modular ERDF Ontologies Equip RDF graphs with modularity constructs as well as declarative rules. A simple modular ERDF ontology [2] is a set of simple r-ERDF ontologies formed by an interface and logic part. Interface Declares exported classes and properties with visibility lists Declares imported classes and properties with import lists (sources of information) Logic part An ERDF graph with negative triples Rules whose bodies are combinations of conjunctions, weak negations (naf) and strong negations (neg) of triples Qualified literals (Lit @ Name) in bodies allow querying of other ontologies 3. Modular Web Framework MWeb defines constructs to allow sharing of knowledge in the Semantic Web [3,4]: Contextualized and global interpretation of arbitrary predicates Explicit control of monotonicity and non- monotonicity of reasoning Scoped open and closed world assumptions Separate interface and implementation of rulebases with modular and independent compilation and loading Two semantics have been proposed [4], MWebWFS and MWebAS, with a solid theory based on the two major semantics of extended logic programming. It is available a compiler into XSB Prolog http://centria.di.fct.unl.pt/~cd/mweb/ :- rulebase ’anne’. :- import('erdf.mw',interface). :- defines global normal class(mw:Vocabulary). :- defines global normal property(choose) visible to 'peter'. :- uses normal class(EUCountry) from 'geo'. :- uses normal property(travel), property(visit) from 'pyr', 'agcy'. :- uses normal class(mw:Vocabulary) from 'pyr', 'agcy’, 'geo’. :- import('erdf.rb',rulebase). ?Package.[choose ->> ?Ctry ] :- neg ( ?Ctry # EUCountry), ?Package.[travel ->> ?Ctry ] @ 'pyr', ?Package.[visit ->> ?City ] @ 'pyr', naf neg ?Package.[visit_other ->> ?City]. … Simple ERDF ontology in MWeb '->'('anne','rdf:type',?S,'EUCountry') :- '->'('geo','rdf:type',?S, 'EUCountry'). '->'('anne','travel',?S,?O) :- '->'('pyr','travel',?S, ?O). '->'('anne','travel',?S,?O) :- '->'('agcy','travel',?S, ?O). '->'('anne','visit',?S,?O) :- '->'('pyr','visit',?S, ?O). '->'('anne','visit',?S,?O) :- '->'('agcy','visit',?S, ?O). '->'('anne', 'rdf:type',?S, 'mw:Vocabulary') :- '->'('pyr', 'rdf:type',... '->'('anne', 'choose', ?Package, ?Ctry) :- neg '#'('anne',?Ctry,'EUCountry'), '->'('pyr', 'travel', ?Package, ?Ctry ), '->'('pyr', 'visit', ?Package, ?City), naf neg '->'('anne','visit_other', ?Package, ?City ). Encoding in extended logic programming :- rulebase 'erdf'.:- rulebase 'rdfs'.:- rulebase 'rdf'.:- rulebase 'rif'. The semantics of ERDF is itself declaratively specified in MWeb rulebases which must be imported by the translated simple r-ERDF ontologies. Schematically, the following four MWeb rulebases are used. Specifies rules defining total and closed classes and properties on top of RDFS. Inheritance of negative extensions. RDFS axiomatic triples, reasoning rules, e.g class and property inheritance. Handles domain and range of properties. Specifies RDF reasoning rules, RDF axiomatic triples and relationship to RIF predefined predicates. Specifies membership and subclass predicates, frames and (partially) equality. 5. Preliminary testing MWebWFS implementation shows superior performance when performing pure RDFS entailment on the Wine ontology 6. Conclusions MWeb is expressive enough to capture all the constructs of simple modular ERDF ontologies Semantics of ERDF reasoning can be declaratively specified by rules expressed in MWeb rulebases The subset of MWeb necessary to capture simple modular ERDF ontologies can be immediately translated into extended logic programming Preliminary benchmarking shows promising results when compared to existing memory-based Semantic Web rule engines. References [1] A. Analyti, G. Antoniou, C. V. Damásio, and G. Wagner, Extended RDF as a Semantic Foundation of Rule Markup Languages, Journal of Artificial Intelligence Research (JAIR), 32, 37–94, (2008). [2] A. Analyti, G. Antoniou, and C. V. Damásio, A Formal Theory for Modular ERDF Ontologies, in Web Reasoning and Rule Systems (RR 2009), volume 5837 of LNCS, pp. 212–226. Springer, (2009). [3] A. Analyti, G. Antoniou, and C. V. Damásio, A Principled Framework for Modular Web Rule Bases and Its Semantics, in Proc. of KR-2008, pp. 390–400. AAAI press, (2008). [4] A. Analyti, G. Antoniou, and C. V. Damásio. MWeb: a Principled Framework for Modular Web Rule Bases and its Semantics. Accepted in ACM Transactions on Computational Logic (TOCL), 2010. cputime (ms) * Mac OS X 10.5.8. 2.93 GHz Intel Core 2 Duo 4Gb 1067 MHz DDR3 Fig. 1 – cputime* for extracting all the triples by several rule engines