Synthese

, Volume 191, Issue 3, pp 371–408

Exploring the tractability border in epistemic tasks

Article

DOI: 10.1007/s11229-012-0215-7

Cite this article as:
Dégremont, C., Kurzen, L. & Szymanik, J. Synthese (2014) 191: 371. doi:10.1007/s11229-012-0215-7

Abstract

We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-hard). In particular, we investigate the impact of assuming information structures to be partition-based (rather than arbitrary relational structures) on the complexity of various problems. We focus on the tractability of concrete epistemic tasks and not on epistemic logics describing them.

Keywords

Epistemic logicComputational complexityEpistemic reasoningMulti-agent systems

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Cédric Dégremont
    • 1
  • Lena Kurzen
    • 2
  • Jakub Szymanik
    • 1
  1. 1.Institute of Artificial IntelligenceUniversity of GroningenGroningenThe Netherlands
  2. 2.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands