Advertisement

NESCOND: An Implementation of Nested Sequent Calculi for Conditional Logics

  • Nicola Olivetti
  • Gian Luca Pozzato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)

Abstract

We present NESCOND, a theorem prover for normal conditional logics. NESCOND implements some recently introduced NESted sequent calculi for propositional CONDitional logics CK and some of its significant extensions with axioms ID, MP and CEM. It also deals with the flat fragment of CK+CSO+ID, which corresponds to the logic C introduced by Kraus, Lehmann and Magidor. NESCOND is inspired by the methodology of leanT A P and it is implemented in Prolog. The paper shows some experimental results, witnessing that the performances of NESCOND are promising. The program NESCOND, as well as all the Prolog source files, are available at http://www.di.unito.it/~pozzato/nescond/

Keywords

Sequent Calculus Nest Sequent Nonmonotonic Reasoning Conditional Logic Proof Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alenda, R., Olivetti, N., Pozzato, G.L.: Nested Sequent Calculi for Conditional Logics. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol. 7519, pp. 14–27. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Alenda, R., Olivetti, N., Pozzato, G.L.: Nested Sequents Calculi for Normal Conditional Logics. Journal of Logic and Computation (to appear)Google Scholar
  3. 3.
    Beckert, B., Posegga, J.: leantap: Lean tableau-based deduction. JAR 15(3), 339–358 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Brünnler, K., Studer, T.: Syntactic cut-elimination for common knowledge. Annals of Pure and Applied Logic 160(1), 82–95 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Fitting, M.: Prefixed tableaus and nested sequents. A. Pure App. Log. 163(3), 291–313 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Goré, R., Postniece, L., Tiu, A.: Cut-elimination and proof-search for bi-intuitionistic logic using nested sequents. In: Advances in Modal Logic, vol. 7, pp. 43–66 (2008)Google Scholar
  7. 7.
    Hausmann, D., Schröder, L.: Optimizing Conditional Logic Reasoning within CoLoSS. Electronic Notes in Theoretical Computer Science 262, 157–171 (2010)CrossRefGoogle Scholar
  8. 8.
    Kashima, R.: Cut-free sequent calculi for some tense logics. St. Logica 53(1), 119–136 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1-2), 167–207 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Lewis, D.: Counterfactuals. Basil Blackwell Ltd. (1973)Google Scholar
  11. 11.
    Nute, D.: Topics in conditional logic. Reidel, Dordrecht (1980)Google Scholar
  12. 12.
    Olivetti, N., Pozzato, G.L.: CondLean 3.0: Improving Condlean for Stronger Conditional Logics. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 328–332. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Olivetti, N., Pozzato, G.L.: Theorem Proving for Conditional Logics: CondLean and GoalDuck. Journal of Applied Non-Classical Logics (JANCL) 18(4), 427–473 (2008)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nicola Olivetti
    • 1
  • Gian Luca Pozzato
    • 2
  1. 1.Aix-Marseille Université, CNRS, LSIS UMR 7296France
  2. 2.Dipartimento di InformaticaUniversitá di TorinoItaly

Personalised recommendations