From Lemma 6 Furthermore , in the proof of Lemma 6.21, it is shown that, We have that d b ([ p[X B ]] + [q[X B ]]) = d b ([ p[X B ] + q ,
Since ? b is the identity mapping, this follows from the correspondence between the boolean operations on elements in B X and boolean operations on supports (cf. Lemma 6.21) More specifically, denote by S and S the carrier sets of T and T , respectively. Furthermore, let, For sb 6 ,
Foundations of Databases, 1995. ,
On the limitations of provenance for queries with difference, Proceedings of the 3rd USENIX Workshop on the Theory and Practice of Provenance, 2011. ,
Provenance for aggregate queries, Proceedings of the 30th symposium on Principles of database systems of data, PODS '11, 2011. ,
DOI : 10.1145/1989284.1989302
URL : http://arxiv.org/abs/1101.1110
The Expressive Power of SPARQL, International Semantic Web Conference, pp.114-129, 2008. ,
DOI : 10.1007/978-3-540-74565-5_14
On the expressiveness of implicit provenance in query and update languages, ACM Transactions on Database Systems, vol.33, issue.28, p.47, 2008. ,
Annotation algebras for RDFS, Proceedings of the 2nd International Workshop on the role of Semantic Web in Provenance Management. CEUR Workshop Proceedings, Article 1, 6 pages. ceur-ws.org, 2011. ,
A Course in Universal Algebra. Number 78 in Graduate Texts in Mathematics, 1981. ,
DOI : 10.1007/978-1-4613-8130-3
Named graphs, Web Semantics: Science, Services and Agents on the World Wide Web, pp.247-267, 2005. ,
DOI : 10.1016/j.websem.2005.09.001
Provenance in Databases: Why, How, and Where, Foundations and Trends in Databases, vol.1, issue.4, pp.379-474, 2009. ,
DOI : 10.1561/1900000006
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.6994
Provenance for SPARQL Queries, Proceedings of the 11th International Conference on the Semantic Web (ISWC'12, pp.625-640, 2012. ,
DOI : 10.1007/978-3-642-35176-1_39
Querying for provenance, trust, uncertainty and other meta knowledge in RDF???, Web Semantics: Science, Services and Agents on the World Wide Web, vol.7, issue.3, pp.204-219, 2009. ,
DOI : 10.1016/j.websem.2009.07.004
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.1875
Annotated XML: Queries and provenance, Proceedings of the 27th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS'08, pp.271-280, 2008. ,
DOI : 10.1145/1376916.1376954
Computers and Intractability: A Guide to the Theory of NP-Completeness, 1979. ,
Vassilis Christophides, and Irini Fundulaki Algebraic structures for capturing the provenance of SPARQL queries, Proceedings of the 16th International Conference on Database Theory (ICDT'13). ACM, pp.153-164, 2013. ,
On database query languages for K-relations, Journal of Applied Logic, vol.8, issue.2, pp.173-185, 2010. ,
DOI : 10.1016/j.jal.2009.09.001
URL : http://doi.org/10.1016/j.jal.2009.09.001
Perm: Processing Provenance and Data on the Same Data Model through Query Rewriting, 2009 IEEE 25th International Conference on Data Engineering, pp.174-185, 2009. ,
DOI : 10.1109/ICDE.2009.15
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.8566
Containment of conjunctive queries on annotated relations, Theory of Computing Systems, pp.429-459, 2011. ,
DOI : 10.1145/1514894.1514930
Provenance semirings, Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems , PODS '07, pp.31-40, 2007. ,
DOI : 10.1145/1265530.1265535
SPARQL 1.1 Query Language, 2013. ,
Specification for tSPARQL, 2008. ,
DOI : 10.1007/978-3-642-02121-3_5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.577
Querying Trust in RDF Data with tSPARQL, Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications (ESWC'09, pp.5-20, 2009. ,
DOI : 10.1007/978-3-642-02121-3_5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.577
Query Evaluation on Probabilistic RDF Databases, Proceedings of the 10th International Conference on Web Information Systems Engineering (WISE'09), pp.307-320, 2009. ,
DOI : 10.1007/978-3-642-04409-0_32
Boolean algebra. A correction, Transactions of the American Mathematical Society, vol.35, issue.2, pp.557-558, 1933. ,
New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell, Transactions of the American Mathematical Society, vol.35, pp.274-304, 1933. ,
Collaborative data sharing via update exchange and provenance, ACM Transactions on Database Systems, vol.38, issue.3, 2013. ,
DOI : 10.1145/2508020.2500127
Querying data provenance, Proceedings of the 2010 international conference on Management of data, SIGMOD '10, pp.951-962, 2010. ,
DOI : 10.1145/1807167.1807269
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.2019
Query answering over incomplete and uncertain RDF, Proceedings of the 17th International Workshop on the Web and Databases, 2014. ,
A Fuzzy Semantics for the Resource Description Framework, Lecture Notes in Computer Science, vol.114, issue.3, pp.244-261, 2008. ,
DOI : 10.1007/3-540-48005-6_7
Prover9 and Mace4, 2005. ,
Semantics and complexity of SPARQL, ACM Transactions on Database Systems, vol.34, issue.16, p.45, 2009. ,
SPARQL Query Language for RDF. www.w3.org/TR/ rdf-sparql-query, 2008. ,
Foundations of SPARQL query optimization, Proceedings of the 13th International Conference on Database Theory, ICDT '10, pp.4-33, 2010. ,
DOI : 10.1145/1804669.1804675
URL : http://arxiv.org/abs/0812.3788
Foundations of Fuzzy Logic and Semantic Web Languages, 2013. ,
DOI : 10.1007/978-3-642-23963-2_2
On Provenance of Queries on Semantic Web Data, IEEE Internet Computing, vol.15, issue.1, pp.31-39, 2011. ,
DOI : 10.1109/MIC.2010.127
The complexity of relational query languages (Extended Abstract), Proceedings of the fourteenth annual ACM symposium on Theory of computing , STOC '82, pp.137-146, 1982. ,
DOI : 10.1145/800070.802186
A general framework for representing, reasoning and querying with annotated Semantic Web data, Web Semantics: Science, Services and Agents on the World Wide Web, vol.11, pp.72-95, 2012. ,
DOI : 10.1016/j.websem.2011.08.006
URL : https://hal.archives-ouvertes.fr/hal-01240838