Modal logic II (M Peliš)


Last update

back to Courses

Modal logic II (Dynamic epistemic logics)

Dpt of Logic, Faculty of Arts, Charles University in Prague
2/0 Zk

The goal of the course is to introduce analyses of knowledge and communication in the framework of modal logics.


  1. Epistemic and dynamic turns in modal logics
    1. Modern modal logic (possible world semantics, E.W.Beth, Saul Kripke)
    2. Kripke-style semantics (transition systems)
    3. Dynamic turn (update semantics, dynamic logic); AI
    4. Epistemology
    5. Reasoning with knowledge
  2. Epistemic logic
    1. Knowledge representation (individual knowledge operators)
    2. Logical omniscience problem, some solutions (awareness fction and non-standard states)
    3. Axioms (K, T, 4, 5, D)
    4. Group knowledge operators: group knowledge, common knowledge, distributed (implicit) knowledge
    5. Common knowledge and non-compactness
    6. Distributed knowledge and two interpretations
    7. Logic of belief (axioms T and D)
    8. Axioms (individual and group knowledge operators)
    9. Bisimulation recalled
  3. Public announcement (PA)
    1. Principles of PA
    2. PA and common knowledge
    3. Successful formulas and updates
    4. Formulas preserved under submodels
    5. PA with belief
  4. Action Models (AM)
    1. Syntax and semantics
    2. Basic properties
    3. Bisimulation and action emulation
    4. Axioms
  5. Expressivity of the introduced dynamic systems' languages (PA, PA+C, AM, AM+C)
  6. Completeness of the introduced systems (S5, S5+C, PA, PA+C, AM, AM+C)


The course is also maintained at Moodle UK under the title Modalni logiky II. There are all recommended papers there. We expect background of an introductory course in modal logic (see, e.g., Blackburn et al.). This course is covered by some chapters of the book (van Ditmarsch et al.).

References - books

  1. J van Benthem. Exploring Logical Dynamics. CSLI Publications, Stanford, 1996.
  2. J van Benthem. Logical Dynamics of Information and Interaction. Cambridge University Press, 2011.
  3. P Blackburn, M de Rijke and Y Venema. Modal Logic. Cambridge Tracts in Theoretical Computer Science, 53, Cambridge University Press, 2001.
  4. H van Ditmarsch, W van der Hoek, B Kooi. Dynamic Epistemic Logic. Springer, 2008.
  5. R Fagin, JY Halpern, Y Moses, MY Vardi. Reasoning about Knowledge. MIT Press, 1995.
  6. D Harrel, D Kozen, J Tiuryn. Dynamic Logic. MIT Press, 2000.
  7. J-J Meyer, W van der Hoek. Epistemic logic for AI and Computer Science. Cambridge, 1995.