Complexity Results of STIT Fragments

Studia Logica 100 (5):1001-1045 (2012)
We provide a Kripke semantics for a STIT logic with the "next" operator. As the atemporal group STIT is undecidable and unaxiomatizable, we are interested in strict fragments of atemporal group STIT. First we prove that the satisfiability problem of a formula of the fragment made up of individual coalitions plus the grand coalition is also NEXPTIME-complete. We then generalize this result to a fragment where coalitions are in a given lattice. We also prove that if we restrict the language to nested coalitions the satisfiability problem is NP-complete if the number of agents is fixed and PSPACE-complete if the number of agents is variable. Finally we embed individual STIT with the "next" operator into a fragment of atemporal group STIT
Keywords STIT logic  Kripke structure  Satisfiability problem  Complexity  Axiomatization
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DOI 10.1007/s11225-012-9445-4
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Emiliano Lorini (2013). Temporal Logic and its Application to Normative Reasoning. Journal of Applied Non-Classical Logics 23 (4):372-399.

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