Alternative axiomatics and complexity of deliberative STIT theories

Details Alternative axiomatics and complexity of deliberative STIT theories Alternative axiomatics and complexity of deliberative STIT theories

2007-04-24

arxiv.org/abs/0704.3238v1

Computer Science

Logic in Computer Science

Submitted to the Journal of Philosophical Logic; 13 pages excluding annex

Scientific paper

10.1007/s10992-007-9078-7

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one 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 the Chellas 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 the Chellas' STIT.

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