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Embeddings of Simple Modular Extended RDF. Carlos V. Damásio 1 , Anastasia Analyti 2 , Grigoris Antoniou 2,3 ( cd@di.fct.unl.pt ), ( analyti@ics.forth.gr ), ( antoniou@ics.forth.gr ). 1 CENTRIA, Dept. Informática da Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa,

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embeddings of simple modular extended rdf

Embeddings of Simple Modular Extended RDF

Carlos V. Damásio1, Anastasia Analyti2, Grigoris Antoniou2,3

(cd@di.fct.unl.pt), (analyti@ics.forth.gr), (antoniou@ics.forth.gr)

1 CENTRIA, Dept. Informática da Faculdade de Ciências e Tecnologia,

Universidade Nova de Lisboa,

2829-516 Caparica, Portugal.

2 Institute of Computer Science, FORTH-ICS,

Crete, Greece.

3 Dept. of Computer Science, Univ. of Crete,

Crete, Greece.

  • Motivation
  • Background: MWebandExtended RDF
  • Simple Modular Extended RDF
  • Example
  • Embedding RIF, RDF, RDFS, and ERDF
  • DirecttranslationintoExtendedLogicProgramming
  • Evaluation
  • Conclusions
  • Knowledge in the Semantic Web must be shared and modularly organised.
  • The 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.

  • Contextualized and global interpretation of arbitrary predicates.
  • Explicit control of monotonicity and non-monotonicity.
  • Scoped open and closed world assumptions.
  • Separate interface and implementation of rulebases with modular and independent compilation and loading.

Two semantics have been proposed, MWebWFSand MWebAS, with a solid theory based on the two major semantics of extended logic programming.

simple modular extended rdf
Simple Modular Extended RDF
  • Equips RDF graphs with modularity constructs and declarative rules.
  • A simple modular ERDF ontology is formed by an interface and logic part [RR 2009].


    • Declares exported classes and properties with visibility lists
    • Declares imported classes and properties with import lists (sources of information)

Logic part

    • An (E)RDF graph which may contain 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 (remote) ontologies
a glimpse of syntax interface
A glimpse of syntax (interface)

:- rulebase 'anne'.:- import('erdf.mw',interface).

% Defined and exported predicates:- defines global normal class(mw:Vocabulary).:- defines global normal property(choose) visible to 'peter'.

% Used (imported) predicates:- uses normal class(EUCountry) from 'geo'.:- uses normal property(travel), property(visit) from 'pyr', 'agcy'.

:- uses normal class(mw:Vocabulary) from 'pyr', 'agcy’, 'geo'.


Importsdefinitionof ERDF interface (includingvocabulary)


a glimpse of syntax rules
A glimpse of syntax (rules)

:- import('erdf.rb',rulebase).

?Package.[choose ->> ?Ctry ] :-

neg ( ?Ctry # EUCountry),

?Package.[travel ->> ?Ctry ] @ 'pyr',

?Package.[visit ->> ?City ] @ 'pyr',

nafneg ?Package.[visit ->> ?City].

Rulesdefiningthesemanticof RIF, RDF, RDFS and ERDF

Triple: ?Subject.[?Property ->> ?Object]

Qualified literal (remotequery)



approach followed
Approach followed
  • The semantics of ERDF is itself declaratively specified in MWebrulebases which must be imported by the translated simple modular ERDF ontologies.

The following four MWebrulebases are used:

  • RIF: specifies membership and subclass predicates, frames and (partially) equality.
  • RDF: specifies RDF reasoning rules, RDF axiomatic triples and relationship to RIF predefined predicates.
  • RDFS: axiomatic triples, RDFS closure rules, e.g class and property inheritance. Handles domain and range of properties.
  • ERDF: Specifies rules defining total and closed classes and properties on top of RDFS. Inheritance of negative extensions.
rif builtins logical part
RIF builtins (logical part)

% RIF member relation

?O # ?CL :- ?O # ?SCL, ?SCL ## ?CL.

neg ?O # ?SCL :-neg ?O # ?CL, ?SCL ## ?CL.

% RIF subclass relation

?C1 ## ?C3 :- ?C1 ## ?C2, ?C2 ## ?C3.

% RIF equality theory.

?T = ?T :- ?T # mw:Vocabulary.?T1 = ?T2 :- ?T2 = ?T1.?T1 = ?T3 :- ?T1 = ?T2, ?T2 = ?T3.

neg ?T1 = ?T2 :- neg ?T2 = ?T1.neg ?T1 = ?T3 :- ?T1 = ?T2, neg ?T2 = ?T3.

% RIF frames obtained by equality reasoning

?O.[?P ->> ?V] :- ?O1.[?P ->> ?V], ?O = ?O1.?O.[?P ->> ?V] :- ?O.[?P1 ->> ?V], ?P = ?P1.?O.[?P ->> ?V] :- ?O.[?P ->> ?V1], ?V = ?V1.

MWebclasscollectingallthevocabularyofthe (current) rulebase

rdf embedding logical part
RDF embedding (logical part)

:- import(rif.rb, rulebase ).

% RDF compatibility with RIF % makes # and rdf:type% equivalent

?X # ?Y :- ?X.[ rdf:type ->> ?Y].?X.[ rdf:type ->> ?Y] :- ?X # ?Y.

% RDF Entailment rule?Z.[ rdf:type ->> rdf:Property] :- ?_.[?Z ->> ?_].

% RDF Axiomatic triples


Previous slide RIF rules are includedinlinehere

rdfs embedding logical part
RDFS embedding (logicalpart)

:- import( 'rdf.rb', rulebase ).

% RDFS compatibility in RIF requires % including ## into rdfs:subClassOf

?X.[rdfs:subClassOf ->> ?Y] :- ?X ## ?Y.

% Some of RDFS entailment rules

?Z.[ rdf:type ->> ?Y] :- ?X.[rdfs:domain ->> ?Y], ?Z.[?X ->> ?W].

?W.[ rdf:type ->> ?Y] :- ?X.[rdfs:range ->> ?Y], ?Z.[?X ->> ?W].

?Z.[ rdf:type ->> ?Y] :- ?X.[rdfs:subClassOf ->> ?Y], ?Z.[rdf:type ->> ?X].

?X.[rdfs:subClassOf ->> ?X] :- ?X.[rdf:type ->> rdfs:Class].

?X.[rdfs:subClassOf ->> ?Z] :- ?X.[rdfs:subClassOf ->> ?Y], ?Y.[rdfs:subClassOf ->> ?Z].

% other entailment rules and triples % follow…

erdf embedding interface
ERDF embedding (interface)

:- rulebase 'http://erdf.org'.:- prefix erdf='http://erdf.org#'.:- import( 'rdfs.mw', interface ).

:- defines internal normal class(erdf:TotalClass),class(erdf:TotalProperty).

:- defines internal normalclass(erdf:PositivelyClosedClass), class(erdf:NegativelyClosedClass). class(erdf:PositivelyClosedProperty),class(erdf:NegativelyClosedProperty).

:- defines internal normal property(erdf:complementOf).

Specificationof total classes andproperties (OWA)

Specificationofclosed classes andproperties (CWA)


erdf embedding logical part
ERDF embedding (logicalpart)
  • Rules to handlestrongnegationextensionsin RIF, RDF and RDFS

% Compatibility with RIFneg ?X # ?Y :-neg ?X.[ rdf:type ->> ?Y].neg ?X.[rdf:type ->> ?Y] :-neg ?X # ?Y.neg ?X.[rdfs:subClassOf ->> ?Y] :- neg ?X ## ?Y.

% Compatibility with RDF?Z.[rdf:type->>rdf:Property] :-neg ?_.[?Z->>?_].

% Downardpropation of negative information in RDFFneg ?Z.[rdf:type ->> ?X] :- ?X.[rdfs:subClassOf->>?Y], neg ?Z.[rdf:type->>?Y].

neg ?Z1.[?X ->> ?Z2] :- ?X.[rdfs:subPropertyOf->>?Y], neg ?Z1.[?Y->>?Z2].

erdf embedding logical part1
ERDF embedding(logicalpart)
  • Total classes

neg ?Z.[rdf:type->>?X] :- ?X.[rdf:type ->> erdf:TotalClass], ?Z #mw:Vocabulary, naf ?Z.[rdf:type->>?X].?Z.[rdf:type->>?X] :- ?X.[rdf:type ->> erdf:TotalClass], ?Z #mw:Vocabulary, nafneg ?Z.[rdf:type->>?X].

  • Closed classes

neg ?Z.[rdf:type->>?X] :- ?X.[rdf:type->>erdf:PositivelyClosedClass], ?Z #mw:Vocabulary, naf ?Z.[rdf:type->>?X].?Z.[rdf:type->>?X] :- ?X.[rdf:type->>erdf:NegativelyClosedClass], ?Z #mw:Vocabulary, nafneg ?Z.[rdf:type->>?X].



translations into elp
Translations into ELP
  • Twotranslationsintoextendedlogicprogramminghavebeendevised.
  • Thefirst uses MWeb'stransformationintoextendedlogicprogrammingand comes for free.
  • Thecurrentprototypeimplementsthistranslationbutintroduces some overheadintheexecution. Evensoitis quite efficientwhencompared to existingalternativesystems (seebelow)
  • A differentalternativepursuedinthepaperisthedefinitionof a directtranslationinto ELP (see ECAI 2010) ofsimple modular ERDF ontologies.
direct translation 1
Direct Translation (1)

Quad '->'('m',p,s,o) predicate to state that triple s p o is true at MWeb rulebase m.

Interface (just use directives are translated)

% Class use'->'('anne','rdf:type',?S,'EUCountry') :- '->'('geo','rdf:type',?S, 'EUCountry').

% Property use'->'('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).

% Vocabulary use'->'('anne', 'rdf:type',?S, 'mw:Vocabulary') :- '->'('pyr', 'rdf:type', ?S, 'mw:Vocabulary').'->'('anne', 'rdf:type',?S, 'mw:Vocabulary') :- '->'('agcy', 'rdf:type', ?S, 'mw:Vocabulary').'->'('anne', 'rdf:type',?S, 'mw:Vocabulary') :- '->'('geo', 'rdf:type', ?S, 'mw:Vocabulary').

direct translation 2
Direct translation (2)

Rules are simpler to translate and basically set the first argument of quads appropriately:

'->'('anne', 'choose', ?Package, ?Ctry) :- neg '#'('anne',?Ctry ,'EUCountry'), '->'('pyr', 'travel', ?Package, ?Ctry ), '->'('pyr', 'visit', ?Package, ?City), naf neg '->'('anne','visit', ?Package, ?City ).

Therulesoftheimported ERDF module are compiledinthesamewayandeachrulebasehasitscopy. Thusclass/propertyextensions are contextualized. Itisalsopossible to makethe a class/property global sharing thedefinitionsinallrulebases.

preliminary testing
Preliminary testing

MWebWFS shows superior performance when performing pure RDFS memory-based entailment on the Wine ontology

cputime (ms)

Fig. 1 – cputime* for extracting all the triples by several rule engines

* Mac OS X 10.5.8. 2.93 GHz Intel Core 2 Duo 4Gb 1067 MHz DDR3

  • MWeb can capture all the constructs of simple modular ERDF ontologies
  • Semantics of ERDF can be declaratively specified in MWeb
  • 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.
  • Subsumptive tabling is preferable (10~100 times faster) and equality reasoning introduces substantial overhead.
  • The MWeb system implementation can be downloaded at


  • OWL2 RL support is underway