Online research in philosophy

(2012). Modal logics for reasoning about infinite unions and intersections of binary relations. Journal of Applied Non-Classical Logics: Vol. 22, No. 4, pp. 275-294. doi: 10.1080/11663081.2012.705960.

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. (shrink)