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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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