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Cut-Free Calculi and Relational Semantics for Temporal STIT Logics

Part of the Lecture Notes in Computer Science book series (LNAI,volume 11468)

Abstract

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for \(\mathsf {Ldm}\), \(\mathsf {Tstit}\) and \(\mathsf {Xstit}\). All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi \(\mathsf {G3Ldm}\) and \(\mathsf {G3Tstit}\) are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also \(\mathsf {Xstit}\) can be characterized through relational frames, omitting the use of BT+AC frames.

Keywords

  • Labelled sequent calculi
  • Cut-free completeness
  • Temporal logic
  • Multi-agent STIT logic
  • Relational semantics

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

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Notes

  1. 1.

    For an introduction to STIT logic and a historical overview we refer to [3, 4, 16].

  2. 2.

    In [22] it is shown that every generalized geometric formula can be captured through (a system of) rules, allowing for the construction of analytic calculi for the minimal modal logic \(\mathsf {K}\) extended with any axioms from the Sahlqvist class. Since all axioms of \(\mathsf {Ldm}\) and \(\mathsf {Xstit}\) are Sahlqvist formulae, the results also apply to these logics.

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Acknowledgments

The authors would like to thank their supervisor Agata Ciabattoni for her helpful comments.

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Correspondence to Kees van Berkel or Tim Lyon .

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van Berkel, K., Lyon, T. (2019). Cut-Free Calculi and Relational Semantics for Temporal STIT Logics. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_52

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  • DOI: https://doi.org/10.1007/978-3-030-19570-0_52

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