An Axiomatic System and a Tableau Calculus for STIT Imagination Logic
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.
KeywordsLogic of imagination STIT logic Canonical models Completeness Axiomatization Tableaux
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.
- 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.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
- 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
- 7.Indrzejczak, A. (2007). Labelled tableaux calculi for weak modal logics. Bulletin of the Section of Logic, 36, 159–171.Google Scholar
- 8.Costa Leite, A. (2010). Logical Properties of Imagination. Abstracta, 6, 103–116.Google Scholar
- 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
- 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.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.