℧-Resolution: An Inference Rule for Regular Multiple-Valued Logics | SpringerLink
Skip to main content
Springer Nature Link
Log in

℧-Resolution: An Inference Rule for Regular Multiple-Valued Logics

  • Conference paper
  • First Online:
Logics in Artificial Intelligence (JELIA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1489))

Included in the following conference series:

Abstract

The inference rule ℧-resolution for regular multiple-valued logics is developed. One advantage of ℧-resolution is that linear, regular proofs are possible. That is, unlike existing deduction techniques, ℧-resolution admits input deductions (for Horn sets) while maintaining regular signs. More importantly, ℧-resolution proofs are at least as short as proofs for definite clauses generated by the standard inference techniques—annotated resolution and reduction—and pruning of the search space occurs automatically.

This research was supported in part by the National Science Foundation under grants CCR-9731893, CCR-9404338 and CCR-9504349.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Baaz, M., and Fermüller, C.G., Resolution-based theorem proving for many-valued logics, J. of Symbolic Computation, 19(4):353–391, 1995.

    Article  MATH  Google Scholar 

  2. Blair, H.A. and Subrahmanian, V.S., Paraconsistent Logic Programming, Theoretical Computer Science, 68:135–154, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  3. Carnielli, W.A., Systematization of finite many-valued logics through the method of tableaux. J. of Symbolic Logic 52(2):473–493, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  4. Davey, B.A., and Priestley, H.A., Introduction to Lattices and Order, Cambridge Mathematical Textbooks, (1990)

    Google Scholar 

  5. Doherty, P., NML3 — A Non-Monotonic Formalism with Explicit Defaults. Linköping Studies in Science and Technology. Dissertations No. 258. Department of Computer and Information Science, Linköping University, 1991.

    Google Scholar 

  6. Fitting, M., First-order modal tableaux, J. Automated Reasoning 4:191–213, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  7. Ginsberg, M.L., Multivalued Logics, Readings in Non-Monotonic Reasoning, 251–255, 1987.

    Google Scholar 

  8. Hähnle, R., Automated Deduction in Multiple-Valued Logics, International Series of Monographs on Computer Science, vol. 10. Oxford University Press, 1994.

    Google Scholar 

  9. Hähnle, R., Short conjunctive normal forms in finitely-valued logics, J. of Logic and Computation, 4(6): 905–927, 1994.

    Article  MATH  Google Scholar 

  10. Hähnle, R., Tableaux methods for many-valued logics, Handbook of Tableau Methods (M d’Agostino, D. Gabbay, R. Hähnle and J. Posegga eds.), Kluwer, Dordrecht. To appear.

    Google Scholar 

  11. Hähnle, R. and Escalada-Imaz, G., Deduction in many-valued logics: a survey, Mathware & Soft Computing, IV(2), 69–97, 1997.

    Google Scholar 

  12. Kifer, M., and Li, A., On the Semantics of Rule-based Expert Systems with Uncertainty, Proceedings of the 2nd International Conference on Database Theory, 102–117, 1988.

    Google Scholar 

  13. Kifer, M., and Lozinskii, E.L., RI: A Logic for Reasoning in Inconsistency, Proceedings of the Fourth Symposium of Logic in Computer Science, Asilomar, 253–262, 1989.

    Google Scholar 

  14. Kifer, M., and Subrahmanian, V.S., Theory of generalized annotated logic programming and its applications, the J. of Logic Programming 12, 335–367, 1992.

    Article  MathSciNet  Google Scholar 

  15. Kifer, M., and Lozinskii, E., A logic for reasoning with inconsistency, J. of Automated Reasoning 9, 179–215, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  16. Lu, J.J., Henschen, L.J., Subrahmanian, V.S., and da Costa, N.C.A., Reasoning in paraconsistent logics, Automated Reasoning: Essays in Honor of Woody Bledsoe (R. Boyer ed.), Kluwer Academic, 181–210, 1991.

    Google Scholar 

  17. Lu, J.J., Nerode, A. and Subrahmanian, V.S. Hybrid Knowledge Bases, IEEE Transactions on Knowledge and Data Engineering, 8(5):773–785, 1996.

    Article  Google Scholar 

  18. Lu, J.J., Murray, N.V., and Rosenthal, E., A Framework for Automated Reasoning in Multiple-Valued Logics, J. of Automated Reasoning 21:39–67, 1998. To appear.

    Article  MATH  MathSciNet  Google Scholar 

  19. Lu, J.J., Logic programming with signs and annotations, J. of Logic and Computation, 6(6):755–778, 1996.

    Article  MATH  Google Scholar 

  20. Murray, N.V., and Rosenthal, E., Adapting classical inference techniques to multiple-valued logics using signed formulas, Fundamenta Informaticae 21:237–253, 1994.

    MATH  MathSciNet  Google Scholar 

  21. Subrahmanian, V.S., On the Semantics of Quantitative Logic Programs, in: Proceedings of the 4th IEEE Symposium on Logic Programming, Computer Society Press, 1987.

    Google Scholar 

  22. Subrahmanian, V.S., Paraconsistent Disjunctive Databases, Theoretical Computer Science, 93, 115–141, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  23. Thirunarayan, K., and Kifer, M., A Theory of Nomonotonic Inheritance Based on Annotated Logic, Artificial Intelligence, 60(1):23–50, 1993.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Brown University, USA

    Sonia M. Leach

  2. Department of Computer Science, Bucknell University, USA

    James J. Lu

  3. Department of Computer Science, State University of New York, USA

    Neil V. Murray

  4. Department of Mathematics, University of New Haven, USA

    Erik Rosenthal

Authors
  1. Sonia M. Leach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James J. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Neil V. Murray
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Erik Rosenthal
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Maryland, College Park, Maryland, 20742, USA

    Jürgen Dix

  2. I.R.I.T. Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse Cedex, France

    Luís Fariñas del Cerro

  3. Fachbereich 4: Informatik, Universität Koblenz, Rheinau 1, D-56075, Koblenz, Germany

    Ulrich Furbach

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Leach, S.M., Lu, J.J., Murray, N.V., Rosenthal, E. (1998). ℧-Resolution: An Inference Rule for Regular Multiple-Valued Logics. In: Dix, J., del Cerro, L.F., Furbach, U. (eds) Logics in Artificial Intelligence. JELIA 1998. Lecture Notes in Computer Science(), vol 1489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49545-2_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-49545-2_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65141-3

  • Online ISBN: 978-3-540-49545-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation