  This work provides proof-search algorithms and automated counter-model
extraction for a class of STIT logics. With this, we answer an open problem
concerning syntactic decision procedures and cut-free calculi for STIT logics.
A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for
multi-agent STIT with at most n-many choices, is introduced. We refine the
calculi G3LdmL^m_n through the use of propagation rules and demonstrate the
admissibility of their structural rules, resulting in auxiliary calculi
Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL
derive theorems within a restricted class of (forestlike) sequents, allowing us
to provide proof-search algorithms that decide single-agent STIT logics. We
prove that the proof-search algorithms are correct and terminate.
