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International Conference on Principles and Practice of Multi-Agent Systems

PRIMA 2019: PRIMA 2019: Principles and Practice of Multi-Agent Systems pp 202–218Cite as

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

Part of the Lecture Notes in Computer Science book series (LNAI,volume 11873)

Abstract

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.

Keywords

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

Work funded by the projects WWTF MA16-028, FWF I2982 and FWF W1255-N23.

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Notes

  1. 1.

    For a discussion of the philosophical utility of reasoning with limited choice see [20].

  2. 2.

    For further information on regular languages and expressions, consult [16].

  3. 3.

    Observe that \(\mathcal {P}_{\varLambda _{1}}(w,u) = \mathcal {P}_{\varLambda _{2}}(w,u)\). Hence, deciding which automaton to employ in determining the side condition is inconsequential: when applying the rule top-down we may consult \(\varLambda _1\), whereas during bottom-up proof-search we may regard \(\varLambda _2\).

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Authors and Affiliations

  1. Institut für Logic and Computation, Technische Universität Wien, 1040, Wien, Austria

    Tim Lyon & Kees van Berkel

Authors
  1. Tim Lyon
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  2. Kees van Berkel
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Correspondence to Tim Lyon .

Editor information

Editors and Affiliations

  1. Università degli Studi di Torino, Turin, Italy

    Matteo Baldoni

  2. Utrecht University, Utrecht, The Netherlands

    Mehdi Dastani

  3. Zhejiang University, Hangzhou, China

    Beishui Liao

  4. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Yuko Sakurai

  5. University of Texas at Dallas, Richardson, TX, USA

    Rym Zalila Wenkstern

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Lyon, T., van Berkel, K. (2019). Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., Zalila Wenkstern, R. (eds) PRIMA 2019: Principles and Practice of Multi-Agent Systems. PRIMA 2019. Lecture Notes in Computer Science(), vol 11873. Springer, Cham. https://doi.org/10.1007/978-3-030-33792-6_13

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  • DOI: https://doi.org/10.1007/978-3-030-33792-6_13

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