Skip to main content
SpringerLink
Log in

Living Books, Automated Deduction and Other Strange Things

  • Chapter
Mechanizing Mathematical Reasoning

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2605))

Abstract

This work is about a “real-world” application of automated deduction. The application is the management of documents (such as mathematical textbooks) as they occur in a readily available tool. These documents are “living”, in the sense, that they can be modified and extended by the reader, who can interact via Living Books with external systems.

A particular task is to assemble a new document from such units in a selective way, based on the user’s current interest and knowledge.

It is argued that this task can be naturally expressed through logic, and that automated deduction technology can be exploited for solving it. More precisely, we rely on first-order clausal logic with some default negation principle, and we propose a model computation theorem prover as a suitable deduction mechanism.

This work is supported by an EU grant TRIAL-SOLUTION and by a BMBF grant In2Math.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Baumgartner, P.: Hyper Tableaux – The Next Generation. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS (LNAI), vol. 1397, pp. 60–76. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  2. Baumgartner, P.: FDPLL – A First-Order Davis-Putnam-Logeman-Loveland Procedure. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 200–219. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Baumgartner, P., Furbach, U.: Automated Deduction Techniques for the Management of Personalized Documents. In: Annals of Mathematics and Artificial Intelligence – Special Issue on Mathematical Knowledge Management. Kluwer Academic Publishers, Dordrecht (2002) (accepted for Publication)

    Google Scholar 

  4. Baumgartner, P., Furbach, U., Niemelä, I.: Hyper Tableaux. In: Orłowska, E., Alferes, J.J., Moniz Pereira, L. (eds.) JELIA 1996. LNCS (LNAI), vol. 1126. Springer, Heidelberg (1996)

    Google Scholar 

  5. Bornscheuer, S.-E.: Rational models of normal logic programs. In: Görz, G., Hölldobler, S. (eds.) KI 1996. LNCS (LNAI), vol. 1137, pp. 1–4. Springer, Heidelberg (1996)

    Google Scholar 

  6. Dix, J., Furbach, U., Niemelä, I.: Nonmonotonic Reasoning: Towards Efficient Calculi and Implementations. In: Voronkov, A., Robinson, A. (eds.) Handbook of Automated Reasoning, pp. 1121–1234. Elsevier-Science- Press, Amsterdam (2001)

    Google Scholar 

  7. Dix, J., Stolzenburg, F.: A framework to incorporate non-monotonic reasoning into constraint logic programming. Journal of Logic Programming 37(1- 3), 47–76 (1998); Special Issue on Constraint Logic Programming. Guest editors: Marriott, K., Stuckey, P.J.

    Article  MATH  MathSciNet  Google Scholar 

  8. Eiter, T., Lu, J., Subrahmanian, V.S.: Computing Non-Ground Representations of Stable Models. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 198–217. Springer, Heidelberg (1997)

    Google Scholar 

  9. Fermüller, C., Leitsch, A.: Hyperresolution and automated model building. Journal of Logic and Computation 6(2), 173–230 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. Furbach, U.: Logic for computer scientists. To appear as Living Book

    Google Scholar 

  11. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of the 5th International Conference on Logic Programming, Seattle, pp. 1070–1080 (1988)

    Google Scholar 

  12. Gottlob, G., Marcus, S., Nerode, A., Salzer, G., Subrahmanian, V.S.: A non-ground realization of the stable and well-founded semantics. Theoretical Computer Science 166(1-2), 221–262 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Graf, P.: ACID User Manual – version 1.0. Technical Report MPI-I-94-DRAFT, Max-Planck- Institut, Saarbrücken, Germany (June 1994)

    Google Scholar 

  14. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for very expressive description logics. Logic Journal of the IGPL 8(3), 239–263 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Letz, R.: Clausal Tableaux. In: Bibel, W., Schmitt, P.H. (eds.) Automated Deduction. A Basis for Applications. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  16. Manthey, R., Bry, F.: SATCHMO: a theorem prover implemented in Prolog. In: Lusk, E., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, pp. 415–434. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  17. Niemelä, I., Simons, P.: Efficient implementation of the well-founded and stable model semantics. In: Proceedings of the Joint International Conference and Symposium on Logic Programming, Bonn, Germany. The MITPress, Cambridge (1996)

    Google Scholar 

  18. Peltier, N.: Pruning the search space and extracting more models in tableaux. Logic Journal of the IGPL 7(2), 217–251 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Robinson, J.A.: Automated deduction with hyperresolution. Internat. J. Comput. Math. 1, 227–234 (1965)

    MATH  MathSciNet  Google Scholar 

  20. Sakama, C.: Possible Model Semantics for Disjunctive Databases. In: Kim, W., Nicholas, J.M., Nishio, S. (eds.) Proceedings First International Conference on Deductive and Object-Oriented Databases (DOOD 1989), pp. 337–351. Elsevier Science Publishers B.V. (North–Holland), Amsterdam (1990)

    Google Scholar 

  21. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48(1), 1–26 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  22. Sagonas, K., Swift, T., Warren, D.S.: An abstract machine for computing the well-founded semantics. Journal of Logic Programming (2000) (to appear)

    Google Scholar 

  23. Stolzenburg, F.: Loop-detection in hyper-tableaux by powerful model generation. Journal of Universal Computer Science 5(3), 135–155 (1999); Special Issue on Integration of Deduction Systems. Guest editors: Hähnle, R., Menzel, W., Schmitt, P.H., Reif, W. Springer, Heidelberg

    MATH  MathSciNet  Google Scholar 

  24. Van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38, 620–650 (1991)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Koblenz-Landau, Koblenz, Germany

    Peter Baumgartner & Ulrich Furbach

Authors
  1. Peter Baumgartner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ulrich Furbach
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. DFKI, Stuhlsatzenhausweg 3, D-66123, Saarbrücken, Germany

    Dieter Hutter

  2. German Research Center for Artificial Intelligence, DFKI GmbH,  

    Werner Stephan

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Baumgartner, P., Furbach, U. (2005). Living Books, Automated Deduction and Other Strange Things. In: Hutter, D., Stephan, W. (eds) Mechanizing Mathematical Reasoning. Lecture Notes in Computer Science(), vol 2605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32254-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-32254-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25051-7

  • Online ISBN: 978-3-540-32254-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation