Compositional Reasoning for Multi-modal Logics

  • Luca Aceto
  • Anna Ingólfsdóttir
  • Cristian Prisacariu
  • Joshua Sack
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7734)


We provide decomposition and quotienting results for multi-modal logic with respect to a composition operator, traditionally used for epistemic models, due to van Eijck et al. (Journal of Applied Non-Classical Logics 21(3–4):397–425, 2011), that involves sets of atomic propositions and valuation functions from Kripke models. While the composition operator was originally defined only for epistemic S5 n models, our results apply to the composition of any pair of Kripke models. In particular, our quotienting result extends a specific result in the above mentioned paper by van Eijck et al. for the composition of epistemic models with disjoint sets of atomic propositions to compositions of any two Kripke models regardless of their sets of atomic propositions. We also explore the complexity of the formulas we construct in our decomposition result.


Model Check Composition Operator Atomic Proposition Kripke Model Epistemic Logic 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Luca Aceto
    • 1
  • Anna Ingólfsdóttir
    • 1
  • Cristian Prisacariu
    • 2
  • Joshua Sack
    • 3
  1. 1.ICE-TCS, School of Computer ScienceReykjavik UniversityReykjavikIceland
  2. 2.Dept. of InformaticsUniv. of OsloBlindernNorway
  3. 3.Institute of Logic, Language, and ComputationUniversity of AmsterdamThe Netherlands

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