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On the Multimodal Logic of Normative Systems

  • Pilar Dellunde
Conference paper
  • 292 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4870)

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 \(\Box_{i}\) and normative system η, we expand the language adding a new modality \(\Box_{i}^{\eta}\) with the intended meaning of \(\Box_{i}^{\eta}\phi\) 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.

Keywords

Fusions of Logics Multimodal Logics Normative Systems Multi-Agent Systems Model Theory Sahlqvist Formulas 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pilar Dellunde
    • 1
  1. 1.Universitat Autònoma de Barcelona and Artificial Intelligence Research Institute (IIIA-CSIC)Cerdanyola del VallesSpain

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