A Computationally Grounded Dynamic Logic of Agency, with an Application to Legal Actions

  • Andreas Herzig
  • Tiago de Lima
  • Emiliano Lorini
  • Nicolas Troquard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7393)


In this article, we propose a Dynamic Logic of Propositional Control DL-PC in which the concept of ‘seeing to it that’ (abbreviated stit) as studied by Belnap, Horty and others can be expressed; more precisely, we capture the concept of the so-called Chellas stit theory and the deliberatibe stit theory, as opposed to Belnap’s original achievement stit. In this logic, the sentence ‘group G sees to it that φ’ is defined in terms of dynamic operators: it is paraphrased as ‘group G is going to execute an action now such that whatever actions the agents outside G can execute at the same time, φ is true afterwards’. We also prove that the satisfiability problem is decidable. In the second part of the article we extend DL-PC with operators modeling normative concepts, resulting in a logic DL-PCLeg. In particular, we define the concepts of ‘legally seeing to it that’ and ‘illegally seeing to it that’. We prove that the decidability result for DL-PC transfers to DL-PCLeg.


Modal logic dynamic logic action agency propositional control 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas Herzig
    • 1
  • Tiago de Lima
    • 2
  • Emiliano Lorini
    • 1
  • Nicolas Troquard
    • 3
  1. 1.University of Toulouse and CNRS, IRITToulouseFrance
  2. 2.University of Artois and CNRSLensFrance
  3. 3.LOA-ISTC-CNRTrentoItaly

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