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.

中文翻译：

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自动化代理推理：STIT 逻辑的证明演算和句法可判定性

这项工作为一类 STIT 逻辑提供了证明搜索算法和自动反模型提取。有了这个，我们回答了一个关于 STIT 逻辑的句法决策程序和无切割演算的开放问题。引入了一类新的无切割完全标记序列演算 G3LdmL^m_n，用于最多有 n 个选择的多智能体 STIT。我们通过使用传播规则细化微积分 G3LdmL^m_n 并证明其结构规则的可接受性，从而产生辅助微积分 Ldm^m_nL。在单智能体的情况下，我们展示了精炼的演算 Ldm^m_nL 在有限的（类森林）序列中推导出定理，使我们能够提供决定单智能体 STIT 逻辑的证明搜索算法。我们证明证明搜索算法是正确的并终止。