[2406.09088] Dyadic obligations: proofs and countermodels via hypersequents
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Computer Science > Logic in Computer Science

arXiv:2406.09088 (cs)
[Submitted on 13 Jun 2024]

Title:Dyadic obligations: proofs and countermodels via hypersequents

Authors:Agata Ciabattoni, Nicola Oliveti, Xavier Parent
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Abstract:The basic system E of dyadic deontic logic proposed by Åqvist offers a simple solution to contrary-to-duty paradoxes and allows to represent norms with exceptions. We investigate E from a proof-theoretical viewpoint. We propose a hypersequent calculus with good properties, the most important of which is cut-elimination, and the consequent subformula property. The calculus is refined to obtain a decision procedure for E and an effective countermodel computation in case of failure of proof search. Using the refined calculus, we prove that validity in E is Co-NP and countermodels have polynomial size.
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2406.09088 [cs.LO]
  (or arXiv:2406.09088v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2406.09088
Related DOI: https://doi.org/10.1007/978-3-031-21203-1_4

Submission history

From: Xavier Parent Dr. [view email]
[v1] Thu, 13 Jun 2024 13:13:29 UTC (39 KB)
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