### Seminar of Non-classical Logics

Marta Bílková and Michal Peli

(Dpt of Logic)
The following list of topics includes my lectures. The full course is maintained at Moodle.

### Epistemic logic

- History in the framework of multi-modal logics
- Kripke semantics for the modality K
- 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

- The meaning of common knowledge in a group of agents ("muddy children" story), everybody knows (group knowledge)
- Kripke semantics for modalities K, E and C
- 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

- Distributed (implicit) knowledge I
- Knowledge as belief (system KD45)
- Predicate epistemic logic

#### References

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

- PAL and PALC (properties and axioms)
- Update
- Public knowledge
- Preservation under submodels
- Relativised common knowledge

#### References

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

- Inferential erotetic logic
- History of erotetic logics
- Questions, direct answers, soundness of questions, safe and risky questions
- Evocation and presuppositions
- Erotetic implication (pure and regular e-implication)
- Comparing questions (giving an answer)
- Reducibility (the role of safe yes-no questions)

- Epistemic logic with questions

#### References

[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 Winiewski. *The Posing of Questions: Logical Foundations of Erotetic Inferences.* Kluwer, 1995.

[3] A Winiewski. Questions and Inferences. *Logique & Analyse*, 173-174-175, pages 5-43, 2001.
#### Handouts

### Semantics of intuitionistic logic

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

#### References

[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 vejdar. *Logika: neúplnost, sloitost 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.