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RESTRICTED INTERPOLATION AND LACK THEREOF IN STIT LOGIC

Published online by Cambridge University Press:  13 September 2019

GRIGORY K. OLKHOVIKOV
GRIGORY K. OLKHOVIKOV*
Affiliation:
Department of Philosophy I, Ruhr University Bochum
*
*DEPARTMENT OF PHILOSOPHY I RUHR UNIVERSITY BOCHUM GA 3/156 UNIVERSITÄTSSTR. 150 D-44780 BOCHUM, GERMANY E-mail: grigory.olkhovikov@rub.de, grigory.olkhovikov@gmail.com
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Abstract

We consider the propositional logic equipped with Chellas stit operators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does not exceed three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic.

Keywords

03C4003B45stit logicinterpolationRobinson Consistency Property
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 3 , September 2020 , pp. 459 - 482
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Copyright
Copyright © Association for Symbolic Logic 2019 

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References

BIBLIOGRAPHY

Balbiani, P., Herzig, A., & Troquard, N. (2008). Alternative axiomatics and complexity of deliberative stit theories. Journal of Philosophical Logic, 37 (4), 387–406.CrossRefGoogle Scholar
Belnap, N., Perloff, M., & Xu, M. (2001). Facing the Future: Agents and Choices in Our Indeterminist World. New York: Oxford University Press.Google Scholar
Broersen, J. (2011). Deontic epistemic stit logic distinguishing modes of mens rea. Journal of Applied Logic, 9(2), 137–152.CrossRefGoogle Scholar
Chang, C. & Keisler, H. (2012). Model Theory. Mineola, NY: Dover.Google Scholar
Chellas, B. F. (1969). The Logical Form of Imperatives. Ph.D. Thesis, Stanford University.Google Scholar
Gabbay, D. & Maksimova, L. (2005). Interpolation and Definability: Modal and Intuitionistic Logics. Oxford Logic Guides. Oxford: Clarendon Press.CrossRefGoogle Scholar
Herzig, A. & Schwarzentruber, F. (2008). Properties of logics of individual and group agency. In Areces, C., and Goldblatt, R., editors. Proceedings of Advances in Modal Logic. London: College Publications, pp. 133–149.Google Scholar
Horty, J. (2001). Agency and Deontic Logic. USA: Oxford University Press.CrossRefGoogle Scholar
Horty, J. F. & Belnap, N. (1995). The deliberative stit: A study of action, omission, ability, and obligation. Journal of Philosophical Logic, 24(6), 583–644.CrossRefGoogle Scholar
Lorini, E. (2013). Temporal logic and its application to normative reasoning. Journal of Applied Non-Classical Logics, 23(4), 372–399.CrossRefGoogle Scholar
Olkhovikov, G. & Wansing, H. (2017). Inference as doxastic agency. Part ii: Ramifications and refinements. Australasian Journal of Logic, 14(4), 408–438.Google Scholar
Olkhovikov, G. & Wansing, H. (2018). Inference as doxastic agency. Part i: The basics of justification stit logic. Studia Logica, 107, 167–194. Online first: https://doi.org/10.1007/s11225-017-9779z.CrossRefGoogle Scholar
van Benthem, J. (1997). Modal foundations for predicate logic. Logic Journal of the IGPL, 5(2), 259–286.CrossRefGoogle Scholar
von Kutschera, F. (1986). Bewirken. Erkenntnis, 24(3), 253–281.CrossRefGoogle Scholar