Department of Electrical Engineering and Computer Science, Iwate University.

Transcription

1 1 RDF RDF Reasoning about RDF and RDF Schema Ken Kaneiwa Department of Electrical Engineering and Computer Science, Iwate University. keywords: Resource Description Framework (RDF), RDF Schema (RDFS), Semantic Web, Deduction System Summary This survey paper describes the syntax and semantics for Resource Description Framework (RDF) and RDF Schema (RDFS). A deduction system for RDF and RDFS is explained as sound and complete for the RDF and RDFS semantics. To develop such a system, we introduce a minimal RDFS fragment, obtained by restricting the syntax of RDF statements, which is simple and provides us with a computationally efficient reasoning algorithm. We also sketch some approaches to an extension of the RDF language and deduction system by involving some Web Ontology Language (OWL) vocabulary. 1. RDF (Resource Description Framework) [Lassila 99] Web Linked Data RDF URI (Uniform Resource Identifier) [Berners-Lee 05] ( ) RDF Web RDF RDF RDF RDF RDF (RDF ) RDF 2 ( ) RDF (2 ) RDF RDF (rdf:type rdfs:subclassof rdfs:subpropertyof ) RDF RDF (RDF entailment rules) RDF RDF Hays [Hayes 04] W3C Web [ 05, Allemang 08, Segaran 09] RDF RDF RDF Web ISWC J.WS RDF RDF RDF RDF RDF RDF ( ) RDF OWL (Web Ontology Language) RDF RDF OWL 2 RDF RDF RDF RDF 3 RDF RDF RDF 4 RDF RDF OWL RDF 5 2. RDF 2 1 RDF? Web Web ( ) URI RDF (RDF )

2 a 2011 person 1 monograph rdf:type rdf:type wrote Tom AIbook1 sells John RDF rdfs:domain rdfs:range person transacts product rdfs:subpropertyof sells rdfs:subclassof rdfs:domain rdfs:range wrote book 2 RDF RDF 2.1 Tom rdf:type person RDF :Tom rdf:type :person. Tom ( ) person Tom person ( ) RDF Web Tom ( ) RDF RDF (RDF [Carroll 05]) 1 RDF RDF AIbook1 (monograph) (person) (wrote ) 1 2 RDF RDF 1 sells transacts (2 ) transacts ( ) ( ) person product (2 )wrote ( ) ( ) person book 1 2 ( ) RDF RDF RDF RDF URI URI U B L 1 OWL RDF ( ) ( ) s U B p U, o U B L RDF s p o. RDF (U B) U (U B L) RDF RDF (s,p,o) RDF G RDF {(s 1,p 1,o 1 ),...,(s n,p n,o n )} 1 2 RDF RDF RDF G G ( G) G RDF RDF s rdfs:subclassof o. s rdfs:subpropertyof o. s rdfs:domain o. s rdfs:range o. 2 s o s o 3 4 s o RDF rdfs URI ( U ) rdfs:subclassof, rdfs:subpropertyof, rdf:type, rdfs:domain rdfs:range sc, sp, type, dom range 2 3 RDF RDF [Hayes 04, Muñoz 09] RDF RDF V ( U L) I I =(IR,IP,IC,Ext,CExt, Lit,I )

3 RDF RDF 3 IR: ( ) IP: IC : ( IC IR) Ext: IP 2 IR IR CExt: IC 2 IR Lit: ( Lit IR) I : (U L) V IR IP RDF (book1,title,aibook1) I I (book1) I (AIbook1) IR I (title) IP title Ext(I (title)) 2 ( IR IR ) (I (book1),i (AIbook1)) Ext(I (title)) I RDF I RDF G G ( ) A:B IR ( ) A G x x U L I A (x)=i (x) x B I A (x)=a(x) A G RDF (s,p,o) I I (p) IP (I A (s),i A (o)) Ext(I (p)) RDF RDF I G (i) x CExt(y) (x,y) Ext(I (type)) (x,y) Ext(I (type)) y IC (x,y) Ext(I (dom)) x IP y IC (x,y) Ext(I (range)) x IP y IC (ii) (x,y) Ext(I (dom)) (u,v) Ext(x) u CExt(y) (x,y) Ext(I (range)) (u,v) Ext(x) v CExt(y) (iii) (x,y) Ext(I (sc)) CExt(x) CExt(y) Ext(I (sc)) IC (iv) (x,y) Ext(I (sp)) Ext(x) Ext(y) Ext(I (sp)) IP 2 RDF G H G H G H (G = H ) 3. RDF RDF RDF RDF 3 1 RDF RDF RDF RDF Web RDF SPARQL (SPARQL Protocol and RDF Query Language) [Prud hommeaux 08] RDF RDF RDF RDF RDF RDF G :transacts rdfs:domain :person. :sells rdfs:subpropertyof :transacts. :John :sells :AIbook1. RDF G RDF :John rdf:type :person. 3 RDF AIbook1 (sells) 2 RDF sells transacts (transacts) 1 RDF transacts person ( ) person W3C RDF (RDF entailment rules) [Marin 04, Horst 05] Horst [Horst 05] RDF ( 2 ) RDF (generalized RDF graph) RDF RDF (U B) (U B) (U B L) Muñoz [Muñoz 09] RDF RDF (U B L) U (U B L) RDF

4 a = [A/Z] A U B L Z B Muñoz 1 4 A B C X Y Z Muñoz 1 RDF URI Z RDF (Z B ) A ( ) Z [A/Z] RDF +1 = [A/Z] RDF A Z 2 (a) (A,sc,B) (B,sc,C) A B B C A C (A,sc,C) +1 3 (a) (A,dom,B) (C,sp,A) (X,C,Y) A B C A C X Y X B (X,type,B) +1 4 (A,sc,B), (B,sc,A), (X,dom,A), (X,range,A) (X,type,A) A (A,sc,A) +1 RDF 1 RDF G G RDF (sp,sp,sp), (sc,sp,sc), (type,sp,type), (dom,sp,dom) (range,sp,range) G 0 G G G 0 0 G n (n 0) G n H ( G n ) G G H RDF RDF 3.1 RDF RDF G H G H G = H RDF RDF RDF G RDF G :Tom :wrote :AIbook1. :Tom rdf:type :person. :AIbook1 rdf:type :monograph. :transacts rdfs:range :product. :book rdfs:subclassof :product. :wrote rdfs:domain :person. :wrote rdfs:range :book. RDF G 1 2 RDF G RDF G 0 G 0 3 G 0 (transacts,dom,person) (sells,sp,transacts) (John,sells,AIbook1) (a) G 0 (John,type,person) G 1 G 1 (sells,sp,transacts) (John,sells,AIbook1) (b) (John,transacts,AIbook1) G 2 G 2 (Tom,wrote, AIbook1) (wrote,sp,wrote) G 3 G 3 (wrote,range,book) (wrote,sp,wrote) (Tom,wrote,AIbook1) (b) G 3 (AIbook1,type,book) G 4 G 4 (book,sc,product) (AIbook1, type,book) (b) G 4 (AIbook1,type,product) G RDF Web RDF RDF RDF 3.1 RDF RDF (s,p,o) s o RDF

5 RDF RDF 5 2 (1) (a) (b) +1 = {(A,sc,C)} {(A,sc,B), (B,sc,C)} (A,sc,C) (a) +1 = {(A,sp,C)} {(A,sp,B), (B,sp,C)} (A,sp,C) +1 = {(X,type,B)} {(A,sc,B), (X,type,A)} (X,type,B) (b) +1 = {(X,B,Y)} {(A,sp,B), (X,A,Y)} (X,B,Y) ( B ) 3 (a) (b) +1 = {(X,type,B)} {(A,dom,B), (C,sp,A), (X,C,Y)} (X,type,B) +1 = {(Y,type,B)} {(A,range,B), (C,sp,A), (X,C,Y)} (Y,type,B) 4 (2) +1 = {(A,sc,A)} (A,sc,B), (B,sc,A), (X,dom,A), (X,range,A) (X,type,A) (A,sc,A) +1 = {(A,sp,A)} (A,sp,B), (B,sp,A), (X,A,Y), (A,dom,X ) (A,range,X ) (A,sp,A)

6 a 2011 G 0 (a) G 1 = G 0 {(John,type,person)} (b) G 2 = G 1 {(John,transacts,AIbook1)} G 3 = G 2 {(wrote,sp,wrote)} (b) G 4 = G 3 {(AIbook1,type,book)} (b) G 5 = G 4 {(AIbook1,type,product)} 3 RDF RDF sc, sp, type, dom range RDF (sp,p,sp) RDF RDF 2 RDF RDF RDF RDF G 1 RDF (s,p,o) 1 RDF RDF G RDF (s,p,o) G G (s,p,o) (G m (s,p,o) ) n 0 (1)(s,p,o) (A,dom,B) (A,range,B) (s,p,o) G (2)(s,p,o) (A,sc,B) A B (A, sc,a 1 ), (A 1,sc,A 2 ),..., (A n,sc,b) (A B ) G (3)(s,p,o) (A,sp,B) A B (A,sp,A 1 ), (A 1,sp,A 2 ),...,(A n,sp,b) (A B ) G (4)(s,p,o) (A,type,B) G (A 1,sc,A 2 ),..., (A n,sc,b) (A 1 B ) (A,C 1,Y) ((A,Y) C 1 ) (C 1,sp,C 2 ),...,(C n,sp,c n+1 ), (C n+1,dom,a 1 ) (C 1 A 1 C n+1 ) (Y,C 1,A) ((Y,A) C 1 ) (C 1,sp,C 2 ),..., (C n,sp,c n+1 ), (C n+1,range, A 1 ) (C 1 A 1 C n+1 ) 2 [Bruijn 07] RDF (A,type,A 1 ) (A A 1 ) (5)(s,p,o) (1)-(4) (s,p,o) G G (s,a 1,o) (A 1,sp,A 2 ),..., (A n,sp,p)(a 1 p ) A = B sc sp A B RDF G 3.3 RDF RDF G 3 G m (AIbook1,type,product) RDF G 4 RDF 4 (s,p,o) (AIbook1,type,product) G (book,sc,product) (Tom,wrote, AIbook1) (wrote,range,book) book product (Tom,AIbook1) wrote wrote book RDF RDF 3.2 RDF RDF G H G m H G = H RDF [Horst 05] RDF G H G = H 3.3 RDF RDF G H G = H NP- RDF G G = H RDF RDF 3.4 RDF RDF G H G m H O( H G log G ) H G RDF G H 4. RDF 4 1 OWL RDF RDF NP RDF

7 RDF RDF 7 Tohmas Tom John owl:sameas 4 rdf:type hasmother Animal owl:somevaluesfrom Mary owl:onproperty rdf:type OWL RDF hasmother Female O( H G log G ) RDF Web OWL(Web Ontology Language) [Patel-Schneider 04] 4 OWL RDF OWL [Horst 05] OWL Full [Baader 07, 09] OWL Lite OWL DL (OWL DL )RDF OWL owl:functionalproperty owl:inversefunctionalproperty owl:symmetricproperty owl:transitiveproperty fun-p inv-fun-p sym-p tra-p 4.1 RDF (hasfather,type,fun-p) hasfather OWL I RDF x CExt(I (fun-p)) (u,v 1 ),(u,v 2 ) Ext(x) (v 1,v 2 ) Ext(I (same)) x CExt(I (inv-fun-p)) (u 1,v),(u 2,v) Ext(x) (u 1,u 2 ) Ext(I (same)) x CExt(I (sym-p)) (u,v) Ext(x) (v,u) Ext(x) x CExt(I (tra-p)) (u,v),(v,w) Ext(x) (u,w) Ext(x) OWL owl:sameas ( same ) OWL 5 (a) RDF (A,type,funp) (Z,A,X ) (Z,A,Y) A (X,same,Y) +1 A Z (X = Y) OWL owl:sameas owl:inverseof owl:equivalentclass owl:equivalentproperty same inv equi-c equi-p RDF (Tom, same,tohmas) same 2 Tom Tohmas OWL I RDF x IC (x IP) (x,y) Ext(I (same)) (x,y) Ext(I (sc)) ((x,y) Ext(I (sp))) x IP (u 1,v 1 ) Ext(x) (u 1,u 2 ) Ext(I (same)) (v 1,v 2 ) Ext(I (same)) (u 2,v 2 ) Ext(x) Ext(I (same)) IR (x,y) Ext(I (inv)) (u,v) Ext(x) (v,u) Ext(y) (x,y) Ext(I (equiv-c)) (x,y) Ext(I (sc)) (y,x) Ext(I (sc)) (x,y) Ext(I (equiv-p)) (x,y) Ext(I (sp)) (y,x) Ext(I (sp)) 6 ( inv 5 (c) ) (c) (c) same equi-c equi-p (a)(b) sc sp (a) RDF (A,sc,B) (B,sc,A) A B (A,equiv-c,B) OWL 4 RDF RDF G 0 G 0 (Tom,type,Animal) (b) G 0 (Animal,same,Animal) G 1 G 1 (Tom,same,Tohmas) (Animal,same,Animal) (Tom,type,Animal)

8 a (a) (b) (c) +1 = {(X,same,Y)} +1 = {(X,same,X)} +1 = {(X,A,Y)} {(A,type,fun-p), (Z,A,X ), (Z,A,Y)} (X,A,Y) {(A,inv,B), (Y,B,X )} {(A,type,inv-fun-p), (X,A,Z), (Y,A,Z)} (Y,A,X ) {(B,inv,A), (Y,B,X )} {(X,same,Z), (Z,same,Y)} (X,same,X) {(A,type,sym-p), (Y,A,X )}, {(Y,same,X)} {(A,type,tra-p), (X,A,Z), (Z,A,Y)} (X,same,Y) {(Z 1,same,X ), (Z 2,same,Y), (Z 1,A,Z 2)} (X,A,Y) 6 (c) (c) +1 = {(A,sc,B)} {(A,same,B), (X,type,A)} (A,equiv-c,B) (B,equiv-c,A) (A,sc,B) (a) +1 = {(A,equiv-c,B)} {(A,sc,B), (B,sc,A)} (A,equiv-c,B) +1 = {(A,sp,B)} {(A,same,B), (X,A,Y)} (A,equiv-p,B) (B,equiv-p,A) (A,sp,B) (b) +1 = {(A,equiv-p,B)} {(A,sp,B), (B,sp,A)} (A,equiv-c,B) G 0 (b) G 1 = G 0 {(Animal,same,Animal)} (c) G 2 = G 1 {(Tohmas,type,Animal)} (a) G 3 = G 2 {(John,type,Animal)} 5 RDF OWL (c) (Tohmas,type,Animal) G 2 ( ) OWL owl:onproperty owl:hasvalue owl:somevaluesfrom owl:allvaluesfrom on-p value some all RDF (Animal, on-p,hasmother) (Animal,some,Female) Animal x y ((x,y) hasmother ) y Female OWL I RDF (x,y 1 ) Ext(I (on-p)) (x,v) Ext(I (value)) u CExt(x) (u, v) Ext(y 1 ) (x,y 1 ) Ext(I (on-p)) (x,y 2 ) Ext(I (some)) (u,v) Ext(y 1 ) v CExt(y 2 ) u CExt(x) (x,y 1 ) Ext(I (on-p)) (x,y 2 ) Ext(I (all)) u CExt(x) (u,v) Ext(y 1 ) v CExt(y 2 ) (x,y 1 ) Ext(I (on-p)) OWL on-p x y 1 value some ( ) all ( ) 7 (a) RDF (A,on-p,B) (A,value,Y) (X,B,Y) B Y X A (X,type,A) +1 (A,onp,B) (A,value,Y) (X,B,Y) X A (a) RDF (A,on-p,B) (A,some,Y) (X,B,Z) (Z,type,Y)

9 RDF RDF G 0 G 2 4 RDF (Animal,on-p,hasMother) (Animal,some,Female) (John,hasMother,Mary) (Mary,type,Animal) (a) (John,type,Animal) G Web RDF RDF RDF [Gutierrez 07] RDF [Analyti 05] RDF OWL Full [Motik 07] ( ) [Pan 07] RDF 1 RDF 5. Web RDF RDF RDF RDF OWL RDF Web RDF RDF OWL RDF RDF RDF RDF Kaufmann (2008) [Analyti 05] Analyti, A., Antoniou, G., Damásio, C. V., and Wagner, G.: Stable Model Theory for Extended RDF Ontologies, in Proceedings of the 8th International Semantic Web Conference (ISWC 2005), LNCS 3729, pp , Springer (2005) [Baader 07] Baader, F., Calvanese, D., McGuinness, D., Nardi, D., and Patel-Schneider, P. eds.: The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge (2nd Edition) (2007) [Berners-Lee 05] Berners-Lee, T., Fielding, R. T., and Masinter, L.: Uniform Resource Identifier (URI): Generic Syntax, (2005) [Bruijn 07] Bruijn, de J. and Heymans, S.: Logical Foundations of (e)rdf(s): Complexity and Reasoning, in Proceedings of the 6th International Semantic Web Conference/2nd Asian Semantic Web Conference (ISWC 2007/ASWC 2007), Busan, Korea, November 11-15, 2007, LNCS 4825, pp , Springer (2007) [Carroll 05] Carroll, J. J., Bizer, C., Hayes, P. J., and Stickler, P.: Named graphs, J. Web Sem., Vol. 3, No. 4, pp (2005) [Gutierrez 07] Gutierrez, C., Hurtado, C. A., and Vaisman, A. A.: Introducing Time into RDF, IEEE Trans. Knowl. Data Eng., Vol. 19, No. 2, pp (2007) [Hayes 04] Hayes, P.: RDF Semantics, W3C Recommendation, (2004) [Horst 05] Horst, ter H. J.: Completeness, decidability and complexity of entailment for RDF Schema and a semantic extension involving the OWL vocabulary, J. Web Sem., Vol. 3, No. 2-3, pp (2005) [ 09] Web, (2009) [ 05] RDF/OWL, (2005) [Lassila 99] Lassila, O. and Swick, R.: Resource Description Framework (RDF) model and syntax specification, W3C Recommendation, (1999) [Marin 04] Marin, D.: A formalization of RDF, Technical Report TR/DCC , Universidad de Chile, (2004) [Motik 07] Motik, B.: On the Properties of Metamodeling in OWL, Journal of Logic and Computation, Vol. 17, No. 4, pp (2007) [Muñoz 09] Muñoz, S., Pérez, J., and Gutierrez, C.: Simple and Efficient Minimal RDFS, J. Web Sem., Vol.7, No.3, pp (2009) [Pan 07] Pan, J. and Horrocks, I.: RDFS(FA): Connecting RDF(S) and OWL DL, IEEE Trans. Knowl. Data Eng., Vol. 19, No. 2, pp (2007) [Patel-Schneider 04] Patel-Schneider, P. F., Hayes, P., and Horrocks, I.: OWL Web Ontology Language Semantics and Abstract Syntax, W3C Recommendation, (2004) [Prud hommeaux 08] Prud hommeaux, E. and Seaborne, A.: SPARQL Query Language for RDF, W3C Recommendation, (2008) [Segaran 09] Segaran, T., Evans, C., and Taylor, J.: Programming the Semantic Web, O Reilly (2009) ( ) ( ) Web UML 2005, ALP [Allemang 08] Allemang, D. and Hendler, J. A.: Semantic Web for the Working Ontologist: Effective Modeling in RDFS and OWL,Morgan

10 a (a) (b) (c) +1 = {(X,type,A)} +1 = {(X,B,Y)} +1 = {(Z,type,Y)} (A,on-p,B) {(A,on-p,B), (X,type,A), {(A,on-p,B), (A,all,Y), {(A,value,Y), (X,B,Y)} (A,value,Y)} (X,B,Z), (X,type,A)} {(A,some,Y), (X,B,Z), (Z,type,Y)} (X,B,Y) (Z,type,Y) (X,type,A)