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A Neutral Temporal Deontic STIT Logic

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11813)

Abstract

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic \(\mathsf {TDS}\). The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic \(\mathsf {TDS}\) sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting.

Keywords

  • Deontic logic
  • Logics of agency
  • Modal logic
  • Multi-agent STIT logic
  • Temporal logic
  • Utilitarianism

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

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Fig. 1.

Notes

  1. 1.

    In future work, we aim to study condition (C3) strengthened to equality, as in [14]. In such a setting, completeness is obtained by proving that each \(\mathsf {TDS}\)-frame can be transformed into a frame (satisfying the same formulae) with strengthened (C3); hence, showing that the logic does not distinguish between the two frame classes.

  2. 2.

    The main reason why the grand coalition operator [Ag] is added to our language, is because it will allow us to axiomatize the no choice between undivided histories principle (see A25 of Definition 4). For a discussion of [Ag] we refer to [14].

  3. 3.

    This also holds when all intersections of choices of agents contain both a 1 and a 0.

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Correspondence to Kees van Berkel .

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van Berkel, K., Lyon, T. (2019). A Neutral Temporal Deontic STIT Logic. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_25

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  • DOI: https://doi.org/10.1007/978-3-662-60292-8_25

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