On the Definability of Simulability and Bisimilarity by Finite Epistemic Models

  • Hans van Ditmarsch
  • David Fernández-Duque
  • Wiebe van der Hoek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6814)


We explore when finite epistemic models are definable up to simulability or bisimulation, either over the basic multi-agent epistemic language \(\mathsf L\) or over its extension \(\mathsf L^C\) with common knowledge operators. Our negative results are that: simulability is not definable in general in \(\mathsf L^C\), and finite epistemic states (i.e., pointed models) are not definable up to bisimulation in \(\mathsf L\). Our positive results are that: finite epistemic states are definable up to bisimulation by model validity of \(\mathsf L\)-formulas, and there is a class of epistemic models we call well-multifounded for which simulability is definable over \(\mathsf L\). From our method it also follows that finite epistemic models (i.e., not-pointed models) are definable up to bisimulation using model validity in \(\mathsf L\). Our results may prove useful for the logical specification of multi-agent systems, as it provides justification for the ubiquitous but often unjustified claims of the form ‘suppose action a can only be performed in state s’: we show when such preconditions exist. An application are characteristic formulae for interpreted systems. They have a special form wherein factual knowledge, positive knowledge, and ignorance can be separated.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hans van Ditmarsch
    • 1
  • David Fernández-Duque
    • 1
  • Wiebe van der Hoek
    • 2
  1. 1.University of SevillaSpain
  2. 2.University of LiverpoolUnited Kingdom

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