Skip to main content
SpringerLink
Log in

Intensional First-Order Logic for P2P Database Systems

  • Chapter
Journal on Data Semantics XII

Part of the book series: Lecture Notes in Computer Science ((JODS,volume 5480))

Abstract

The meaning of concepts and views defined over a database ontology can be considered as intensional objects which have a particular extension in a given possible world: for instance in the actual world. Thus, non invasive mapping between completely independent peer databases in a P2P systems can be naturally specified by the set of couples of views, which have the same meaning (intension), over two different peers. Such a kind of mapping has very different semantics from standard view-based mappings based on material implication, commonly used for Data Integration Systems. The introduction of an intensional equivalence generates the quotient intensional FOL fundamental for a query answering in P2P systems. In this paper we introduce this formal intensional FOL by fusing Bealer’s intensional algebraic FOL with a possible-world semantics of the Montague’s FOL modal approach to natural language. We modify the Bealer’s intensional algebra in order to deal with relational databases and views, by introducing the join operation of relational algebra. Then we adopt the S5 Kripke frame in order to define an intensional equivalence relation between views for peer databases. Finally, we define an embedding of P2P database system into this quotient intensional FOL, and the computing of its extensionalization mapping in the actual Montague’s world.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ushold, M.: Where is the semantics in the semantic web. In: Workshop on Ontologies in Agent Systems (OAS) at the 5th International Conference on Autonomous Agents (2001)

    Google Scholar 

  2. Gribble, S., Halevy, A., Ives, Z., Rodrig, M., Suciu, D.: What can databases do for Peer-to-Peer? In: WebDB Workshop on Databases and the Web (2001)

    Google Scholar 

  3. Serafini, L., Giunchiglia, F., Mylopoulos, J., Bernstein, P.A.: The local relational model: Model and proof theory. Technical Report 0112-23, ITC-IRST (2001)

    Google Scholar 

  4. Ghidini, C., Giunchiglia, F.: Local models semantics or contextual reasoning = locality + compatibility. Artificial Intelligence 127, 221–259 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Reiter, R.: Towards a logical reconstruction of relational database theory. In: Brodie, M.L., Mylopoulos, J., Schmidt, J.W. (eds.) On Conceptual Modeling: Perspectives from Artificial Intelligence Databases and Programming Languages (1984)

    Google Scholar 

  6. Majkić, Z.: Weakly-coupled ontology integration of P2P database systems. In: 1st Int. Workshop on Peer-to-Peer Knowledge Management (P2PKM), Boston, USA, August 22 (2004)

    Google Scholar 

  7. Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Logical foundations of Peer-to-Peer data integration. In: PODS 2004, Paris, France, June 14-16 (2004)

    Google Scholar 

  8. Lenzerini, M., Majkić, Z.: General framework for query reformulation. Semantic Webs and Agents in Integrated Economies, D3.1, IST-2001-34825 (February 2003)

    Google Scholar 

  9. Franconi, E., Kuper, G., Lopatenko, A., Serafini, L.: A robust logical and computational characterization of Peer-to-Peer data systems. Technical Report DIT-03-051, University of Trento, Italy (September 2003)

    Google Scholar 

  10. Bealer, G.: Universals. The Journal of Philosophy 90, 5–32 (1993)

    Article  MathSciNet  Google Scholar 

  11. Bealer, G.: A solution to Frege’s puzzle. In: Tomberlin, J. (ed.) Philosophical Perspectives, vol. 7, pp. 17–61. Ridgeview Press, Atascadero (1993)

    Google Scholar 

  12. Chen, W., Kifer, M., Warren, D.S.: HiLog: A foundation for higher-order logic programming. Journal of Logic Programming 15, 187–230 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  13. Calvanese, D., Damaggio, E., De Giacomo, G., Lenzerini, M., Rosati, R.: Semantic data integration in P2P systems. In: Proc. of the Int. Workshop On Databases, Inf. Systems and P2P Computing, Berlin, Germany (September 2003)

    Google Scholar 

  14. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Inconsistency tollerance in P2P data integration: an epistemic approach. In: Proc. 10th Int. Workshop on Database Programming Language (2005)

    Google Scholar 

  15. Majkić, Z.: Intensional semantics for P2P data integration. In: LNCS Journal on Data Semantics VI, Special Issue on ‘Emergent Semantics’, April 15 (2006)

    Google Scholar 

  16. Majkić, Z.: Weakly-coupled P2P system with a network repository. In: 6th Workshop on Distributed Data and Structures (WDAS 2004), Lausanne, Switzerland, July 5-7 (2004)

    Google Scholar 

  17. Majkić, Z.: Massive parallelism for query answering in weakly integrated P2P systems. In: Workshop GLOBE 2004, Zaragoza, Spain, August 30-September 3 (2004)

    Google Scholar 

  18. Majkić, Z.: Intensional logic and epistemic independency of intelligent database agents. In: 2nd International Workshop on Philosophy and Informatics (WSPI 2005), Kaiserslautern, Germany, April 10-13 (2005)

    Google Scholar 

  19. Majkić, Z.: Non omniscient intensional contextual reasoning for query-agents in P2P systems. In: 3rd Indian International Conference on Artificial Intelligence (IICAI 2007), Pune, India, December 17-19 (2007)

    Google Scholar 

  20. Majkić, Z., Prasad, B.: Soft query-answering computing in P2P systems with epistemically independent peers. In: Book on Soft Computing Applications in Industry. STUDFUZZ, vol. 226, pp. 331–356. Springer, Berlin (2008)

    Chapter  Google Scholar 

  21. Lenzerini, M.: Data integration: A theoretical perspective, pp. 233–246 (2002)

    Google Scholar 

  22. Greco, G., Greco, S., Zumpano, E.: A logic programming approach to the integration, repairing and querying of inconsistent databases. In: Codognet, P. (ed.) ICLP 2001. LNCS, vol. 2237, pp. 348–364. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  23. Gelfond, M., Lifshitz, V.: The stable model semantics for logic programming. In: Proc. of the Fifth Logic Programming Symposium, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  24. Majkić, Z.: Plausible query-answering inference in data integration. In: 18th International Florida Artificial Intelligence Conference (FLAIRS 2005), Clearwater Beach, USA, May 15-17 (2005)

    Google Scholar 

  25. Majkić, Z.: Fixpoint semantics for query answering in data integration systems. In: AGP 2003 - 8.th Joint Conference on Declarative Programming, Reggio Calabria, pp. 135–146 (2003)

    Google Scholar 

  26. Majkić, Z.: Autoepistemic logic programming for reasoning with inconsistency. In: International Symposium on Logic-based Program Synthesis and Transformation (LOPSTR), Imperial College, London, UK, September 7-9 (2005)

    Google Scholar 

  27. Blackburn, P.: Representation, reasoning, and relational structures: a hybrid logic manifesto. Methods for Modalities 1, Logic Journal of the IGPL 8, 339–365 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  28. Bealer, G.: Theories of properties, relations, and propositions. The Journal of Philosophy 76, 634–648 (1979)

    Article  Google Scholar 

  29. Bealer, G.: Quality and concept. Oxford University Press, USA (1982)

    Book  Google Scholar 

  30. Lewis, D.K.: On the prularity of worlds. Blackwell, Oxford (1986)

    Google Scholar 

  31. Stalnaker, R.: Inquiry. MIT Press, Cambridge (1984)

    Google Scholar 

  32. Montague, R.: Universal grammar. Theoria 36, 373–398 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  33. Montague, R.: The proper treatment of quantification in ordinary English. In: Hintikka, J., et al. (eds.) Approaches to Natural Language, pp. 221–242. Reidel, Dordrecht (1973)

    Chapter  Google Scholar 

  34. Montague, R.: Formal philosophy. In: Thomason, R. (ed.) selected papers of Richard Montague, pp. 108–221. Yale University Press, New Haven (1974)

    Google Scholar 

  35. Lembo, D., Lenzerini, M., Rosati, R.: Source inconsistency and incompleteness in data integration. CEUR Electronic Workshop Proceedings (2002), http://ceur-ws.org/Vol-54/

  36. Majkić, Z.: Querying with negation in data integration systems. In: 9th International Database Engineering and Application Symposium (IDEAS), Montreal, Canada, July 25-27, pp. 58–70. IEEE Computer Society, Los Alamitos (2005)

    Chapter  Google Scholar 

  37. Levy, A., Mendelzon, A., Sagiv, Y.: Answering queries using views. In: Proc. 14th ACM Symp. on Principles of Database Systems, pp. 95–104 (1995)

    Google Scholar 

  38. Majkić, Z.: Coalgebraic specification of query computation in intensional P2P database systems. In: Int. Conference on Theoretical and Mathematical Foundations of Computer Science (TMFCS 2008), Orlando FL, USA, July 9-11 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ETF, Applied Mathematics Department, University of Belgrade, Serbia

    Zoran Majkić

Authors
  1. Zoran Majkić
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. EPFL-IC, Database Laboratory, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Stefano Spaccapietra

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Majkić, Z. (2009). Intensional First-Order Logic for P2P Database Systems. In: Spaccapietra, S. (eds) Journal on Data Semantics XII. Lecture Notes in Computer Science, vol 5480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00685-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00685-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00684-5

  • Online ISBN: 978-3-642-00685-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation