Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics

摘要

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 G3Ldm_n~m, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3Ldm_n~m through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in the auxiliary calculi Ldm_n~mL. In the single-agent case, we show that the refined calculi Ldm_n~mL 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.