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

TL;DR

This paper develops proof-search algorithms and cut-free calculi for multi-agent STIT logics, solving an open problem in syntactic decision procedures and enabling automated reasoning and counter-model extraction.

Contribution

It introduces a new class of cut-free labelled sequent calculi for multi-agent STIT logics and proves their correctness and termination for decision procedures.

Findings

Introduced the G3LdmL^m_n calculi for multi-agent STIT logics.

Proved the admissibility of structural rules and the derivability within restricted sequents.

Provided correct and terminating proof-search algorithms for single-agent STIT logics.

Abstract

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.