Advertisement

VINTE: An Implementation of Internal Calculi for Lewis’ Logics of Counterfactual Reasoning

  • Marianna Girlando
  • Björn Lellmann
  • Nicola Olivetti
  • Gian Luca Pozzato
  • Quentin Vitalis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10501)

Abstract

We present VINTE, a theorem prover for conditional logics for counterfactual reasoning introduced by Lewis in the seventies. VINTE implements some internal calculi recently introduced for the basic system \(\mathbb {V}\) and some of its significant extensions with axioms \(\mathbb {N}\), \(\mathbb {T}\), \(\mathbb {C}\), \(\mathbb {W}\) and \(\mathbb {A}\). VINTE is inspired by the methodology of Open image in new window and it is implemented in Prolog. The paper shows some experimental results, witnessing that the performances of VINTE are promising.

References

  1. 1.
    Alenda, R., Olivetti, N., Pozzato, G.L.: Nested sequent calculi for normal conditional logics. J. Log. Comput. 26(1), 7–50 (2016)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Baltag, A., Smets, S.: The logic of conditional doxastic actions. Texts Log. Games 4, 9–31 (2008). Special Issue on New Perspectives on Games and InteractionMathSciNetGoogle Scholar
  3. 3.
    Beckert, B., Posegga, J.: leanTAP: lean tableau-based deduction. J. Autom. Reason. 15(3), 339–358 (1995)CrossRefMATHGoogle Scholar
  4. 4.
    Board, O.: Dynamic interactive epistemology. Games Econ. Behav. 49(1), 49–80 (2004)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Genovese, V., Giordano, L., Gliozzi, V., Pozzato, G.L.: Logics in access control: a conditional approach. J. Log. Comput. 24(4), 705–762 (2014)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Girlando, M., Lellmann, B., Olivetti, N., Pozzato, G.L.: Standard sequent calculi for Lewis’ logics of counterfactuals. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS, vol. 10021, pp. 272–287. Springer, Cham (2016). doi: 10.1007/978-3-319-48758-8_18 CrossRefGoogle Scholar
  7. 7.
    Girlando, M., Lellmann, B., Olivetti, N., Pozzato, G.L.: Hypersequent calculi for Lewis’ conditional logics with uniformity and reflexivity. In: Nalon, C., Schmidt, R.A. (eds.) TABLEAUX 2017. LNCS (LNAI), vol. 10501, pp. 131–148. Springer, Cham (2017)Google Scholar
  8. 8.
    Grahne, G.: Updates and counterfactuals. J. Log. Comput. 8(1), 87–117 (1998)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Lewis, D.: Counterfactuals. Blackwell, Hoboken (1973)MATHGoogle Scholar
  11. 11.
    Nute, D.: Topics in Conditional Logic. Reidel, Dordrecht (1980)CrossRefMATHGoogle 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). doi: 10.1007/11554554_27 CrossRefGoogle Scholar
  13. 13.
    Olivetti, N., Pozzato, G.L.: Theorem proving for conditional logics: condlean and goalduck. J. Appl. Non-Class. Log. 18(4), 427–473 (2008)CrossRefMATHGoogle Scholar
  14. 14.
    Olivetti, N., Pozzato, G.L.: NESCOND: an implementation of nested sequent calculi for conditional logics. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 511–518. Springer, Cham (2014). doi: 10.1007/978-3-319-08587-6_39 Google Scholar
  15. 15.
    Olivetti, N., Pozzato, G.L.: Nested sequent calculi and theorem proving for normal conditional logics: the theorem prover NESCOND. Intelligenza Artificiale 9(2), 109–125 (2015)CrossRefGoogle Scholar
  16. 16.
    Olivetti, N., Pozzato, G.L.: A standard internal calculus for Lewis’ counterfactual logics. In: Nivelle, H. (ed.) TABLEAUX 2015. LNCS, vol. 9323, pp. 270–286. Springer, Cham (2015). doi: 10.1007/978-3-319-24312-2_19 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Marianna Girlando
    • 1
  • Björn Lellmann
    • 2
  • Nicola Olivetti
    • 1
  • Gian Luca Pozzato
    • 3
  • Quentin Vitalis
    • 4
  1. 1.Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LSIS UMR 7296MarseilleFrance
  2. 2.Technische Universität WienViennaAustria
  3. 3.Dipartimento di InformaticaUniversitá di TorinoTurinItaly
  4. 4.Département InformatiqueÉcole Spéciale Militaire de Saint-CyrGuerFrance

Personalised recommendations