Journal of Philosophical Logic

, Volume 47, Issue 2, pp 259–279 | Cite as

An Axiomatic System and a Tableau Calculus for STIT Imagination Logic

Article

Abstract

We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing (2015). Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.

Keywords

Logic of imagination STIT logic Canonical models Completeness Axiomatization Tableaux 

Notes

Acknowledgments

We would like to thank the two anonymous referees for their valuable comments, and we would like to acknowledge financial support from the DFG, project WA 936/11-1, during the preparation of the revised version of this paper. Grigory Olkhovikov would like to acknowledge financial support from the Alexander von Humboldt Foundation which made it possible for him to take part in obtaining the results reported above.

References

  1. 1.
    Balbiani, P., Herzig, A., & Troquard, N. (2008). Alternative axiomatics and complexity of deliberative STIT theories. Journal of Philosophical Logic, 37, 387–406.CrossRefGoogle Scholar
  2. 2.
    Belnap, N.D., Perloff, M., & Xu, M. (2001). Facing the Future: Agents and Choices in our Indeterminist World. Oxford: Oxford UP.Google Scholar
  3. 3.
    Broersen, J. (2009). A complete STIT logic for knowledge and action, and some of its applications. In Baldoni, M. et al. (Eds.) Proceedings declarative agent languages and technologies VI, 6th International Workshop DALT 2008, Lecture Notes in Artificial Intelligence, (Vol. 5397 pp. 47–59). Berlin: Springer.Google Scholar
  4. 4.
    Chellas, B. (1980). Modal logic an introduction. Cambridge: Cambridge UP.CrossRefGoogle Scholar
  5. 5.
    Herzig, A., & Schwarzentruber, F. (2008). Properties of logics of individual and group agency. In Areces, C., & Goldblatt, R. (Eds.) Advances in modal logic, (Vol. 7 pp. 133–149). London: College Publications.Google Scholar
  6. 6.
    Horty, J. (2001). Agency and deontic logic. New York: Oxford UP.CrossRefGoogle Scholar
  7. 7.
    Indrzejczak, A. (2007). Labelled tableaux calculi for weak modal logics. Bulletin of the Section of Logic, 36, 159–171.Google Scholar
  8. 8.
    Costa Leite, A. (2010). Logical Properties of Imagination. Abstracta, 6, 103–116.Google Scholar
  9. 9.
    Lorini, E., & Schwarzentruber, F. (2011). A logic for reasoning about counterfactual emotions. Artificial Intelligence, 175, 814–847.CrossRefGoogle Scholar
  10. 10.
    Niiniluoto, I. (1985). Imagination and fiction. Journal of Semantics, 4, 209–222.CrossRefGoogle Scholar
  11. 11.
    Priest, G. (2005). Towards non-being: The logic and metaphysics of intentionality. Oxford: Oxford UP.CrossRefGoogle Scholar
  12. 12.
    Priest, G. (2008). An introduction to Non-Classical logic from if to is. Cambridge: Cambridge UP.CrossRefGoogle Scholar
  13. 13.
    Williamson, T. (2016). Knowing and imagining. In Kind, A., & Kung, P. (Eds.) Knowledge through Imagination (pp. 113–123). Oxford: Oxford UP.CrossRefGoogle Scholar
  14. 14.
    Xu, M. (2015). Combinations of stit with ought and know. Journal of Philosophical Logic, 44, 851–877.CrossRefGoogle Scholar
  15. 15.
    Semmling, C., & Wansing, H. (2011). Reasoning about Belief Revision. In Olsson, E. J., & Enqvist, S. (Eds.) Belief Revision meets Philosophy of Science (pp. 303–328). Dordrecht: Springer.Google Scholar
  16. 16.
    Wansing, H. (2006a). Doxastic decisions, epistemic justification, and the logic of agency. Philosophical Studies, 128, 201–227.CrossRefGoogle Scholar
  17. 17.
    Wansing, H. (2006b). Tableaux for Multi-agent Deliberative-stit Logic. In Governatori, G., Hodkinson, I., & Venema, Y. (Eds.) Advances in Modal Logic, (Vol. 6 pp. 503–520). London: King’s College Publications.Google Scholar
  18. 18.
    Wansing, H. (2015). Remarks On the logic of imagination. A step towards understanding doxastic control through imagination. Synthese. doi: 10.1007/s11229-015-0945-4.

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Philosophy IIRuhr-University BochumBochumGermany
  2. 2.Department of PhilosophyUral Federal UniversityEkaterinburgRussia

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