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

  • Tim LyonEmail author
  • Kees van Berkel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11873)


This work provides proof-search algorithms and automated counter-model extraction for a class of \(\mathsf {STIT}\) logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for \(\mathsf {STIT}\) logics. A new class of cut-free complete labelled sequent calculi \(\mathsf {G3Ldm}_{n}^{m}\), for multi-agent \(\mathsf {STIT}\) with at most n-many choices, is introduced. We refine the calculi \(\mathsf {G3Ldm}_{n}^{m}\) through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in the auxiliary calculi \(\mathsf {Ldm}_{n}^{m}\mathsf {L}\). In the single-agent case, we show that the refined calculi \(\mathsf {Ldm}_{n}^{m}\mathsf {L}\) derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent \(\mathsf {STIT}\) logics. We prove that the proof-search algorithms are correct and terminate.


Decidability Labelled calculus Logics of agency Proof search Proof theory Propagation rules Sequent \(\mathsf {STIT}\) logic 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für Logic and ComputationTechnische Universität WienWienAustria

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