Seminar of Non-classical Logics

Marta Bílková and Michal Peliš
(Dpt of Logic)

The following list of topics includes my lectures. The full course is maintained at Moodle.

Epistemic logic

  1. History in the framework of multi-modal logics
  2. Kripke semantics for the modality K
  3. Axiomatic systems based on modal logics (K, T, S4, S5)
  4. The meaning of common knowledge in a group of agents ("muddy children" story), everybody knows (group knowledge)
  5. Kripke semantics for modalities K, E and C
  6. Axiomatic systems for modalities K, E and C
  7. Distributed (implicit) knowledge I
  8. Knowledge as belief (system KD45)
  9. Predicate epistemic logic


R Fagin, JY Halpern, Y Moses, MY Vardi. Reasoning About Knowledge. MIT Press, 1995.
J-J Meyer, W van der Hoek. Epistemic logic for AI and Computer Science. Cambridge, 1995.

Public announcement logic

  1. PAL and PALC (properties and axioms)
  2. Update
  3. Public knowledge
  4. Preservation under submodels
  5. Relativised common knowledge


J van Benthem, J van Eijck, B Kooi. Logics of Communication and Change. (web)
H van Ditmarsch, W van der Hoek, B Kooi. Dynamic Epistemic Logic. Springer, 2008.

Logic of questions

  1. Inferential erotetic logic
  2. Epistemic logic with questions


[1] D Harrah. The Logic of Questions. In D Gabbay and F Guenthner, editors, Handbook of Philosophical Logic, volume 8, pages 1-60, Kluwer, 2002.
[2] A Wiœniewski. The Posing of Questions: Logical Foundations of Erotetic Inferences. Kluwer, 1995.
[3] A Wiœniewski. Questions and Inferences. Logique & Analyse, 173-174-175, pages 5-43, 2001.


Semantics of intuitionistic logic

  1. Algebraic semantics. Heyting algebras. [1,3,5]
  2. Kripke semantics. Equivalence of algebraic and Kripke validity. [3]
  3. Beth tableaus. Tree-type possible-world semantics based on Beth tableaus. [3]
  4. Kripke frames and models. Truth-preserving operations (generation, p-morphism, disjoint union of frames). [1]
  5. Origins of intuitionistic semantics. [5]


[1] A Chagrov, M Zakharyaschev. Modal Logic. Clarendon Press, Oxford, 1997.
[2] M Dummett. Elements of Intuitionism. Clarendon Press, Oxford, 1997. Second Edition.
[3] M Fitting. Intuitionistic Logic, Model Theory and Forcing. North-Holland, 1969.
[4] V Švejdar. Logika: neúplnost, složitost a nutnost. Academia, Praha, 2002.
[5] D van Dalen. Intuitionistic Logic. In D Gabbay and F Guenthner, editors, Handbook of Philosophical Logic, volume 3, pages 225-339, D.Reidel, 1986.