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Dynamic logic

Topics

1. Dynamic epistemic logic
   1. Dynamic logic and programmes
   2. Change of information
2. 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)
      • Knowledge and truth, positive and negative introspection
      • Completeness theorem, canonical model and max-consistent sets of formulas (Lindenbaum lemma)
      • Canonicity
      • Decidability via finite models (+ the role of filtration), problems with accessibility relations
   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
      • Non-canonicity, non-compactness, accessibility realation for C, quasi-canonical model
      • Weak completeness theorem via finite canonical model
   7. Distributed (implicit) knowledge I
   8. Knowledge as belief (system KD45)
   9. Predicate epistemic logic
3. Public announcement logic (PAL)
   1. PAL - properties and axioms (S5 version)
   2. PAL with common knowledge (PALC)
   3. Successful and unsuccessful formulas and updates
   4. Public announcement for weaker systems
   5. Relativised common knowledge
4. Relevant epistemic logic
5. Logic for communication
   1. Logic of questions
   2. Epistemic logic with questions
   3. Questions in PAL

Study

References

1. J van Benthem. Exploring Logical Dynamics. CSLI Publications, Stanford, 1996.
2. H van Ditmarsch, W van der Hoek, B Kooi. Dynamic Epistemic Logic. Springer, 2008. (A,B,C)
3. R Fagin, JY Halpern, Y Moses, MY Vardi. Reasoning about Knowledge. MIT Press, 1995. (B)
4. D Harrel, D Kozen, J Tiuryn. Dynamic Logic. MIT Press, 2000. (A)
5. J-J Meyer, W van der Hoek. Epistemic logic for AI and Computer Science. Cambridge, 1995. (B)