On the multimodal logic of normative systems

  • Authors:
  • Pilar Dellunde

  • Affiliations:
  • Universitat Autònoma de Barcelona and Artificial Intelligence Research Institute, CSIC, Catalonia, Spain

  • Venue:
  • COIN'07 Proceedings of the 2007 international conference on Coordination, organizations, institutions, and norms in agent systems III
  • Year:
  • 2007

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Abstract

We introduce Multimodal Logics of Normative Systems as a contribution to the development of a general logical framework for reasoning about normative systems over logics for Multi-Agent Systems. Given a multimodal logic L, for every modality □i and normative system η, we expand the language adding a new modality □iη with the intended meaning of □iηΦ being "Φ is obligatory in the context of the normative system η over the logic L". In this expanded language we define the Multimodal Logic of Normative Systems over L, for any given set of normative systems N, and we give a sound and complete axiomatisation for this logic, proving transfer and model checking results. The special case when L and N are axiomatised by sets of Sahlqvist or shallow modal formulas is studied.