Alternative axiomatics and complexity of deliberative stit theories

Journal of Philosophical Logic 37 (4):387 - 406 (2008)
Abstract
We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT.
Keywords axiomatization  complexity  logic of agency  STIT
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Citations of this work BETA
Ming Xu (2010). Combinations of Stit and Actions. Journal of Logic, Language and Information 19 (4):485-503.
Ming Xu (2012). Actions as Events. Journal of Philosophical Logic 41 (4):765 - 809.
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