Practicalities

Instructors: Jialiang Yan, emails: cu252023@cupl.edu.cn

Time and Place: 

Assessment : 

Final exam: 

More specific information about homework and grading: Deadlines for submission are strict; this applies in particular to the condition that homework should be handed in at the beginning of class. Homework handed in after the deadline will not be taken into consideration. Unless explicitly specified otherwise, you are allowed to collaborate with your fellow students, on the following conditions:

you can only work in small groups of at most three people;

you can discuss the exercises together, but you have to write down the solution individually;

you must explicitly write on your homework with whom you have been working together.

never prove statements that are explicitly mentioned in the lecture notes (unless specifically asked otherwise); simply refer to these results if you use them;

in the case of a routine argument, you do not need to go into all the technical details;

in case of proofs by induction on the complexity of formulas, one or two cases will usually suffice.

About the course

  • Objectives:
    • The students should be able to point out when a modal formula is satisfied/valid on a given Kripke model/frame.
    • They should also be able to compute standard translations of modal formulas and first-order correspondents of Sahlqvist formulas.
    • They are expected to produce a completeness proof via the canonical model construction for some basic systems of modal logic.
    • Students are also expected to solve basic problems involving more complex modal systems such as PDL.
  • Contents: The course covers the basic notions of modal logic:
    • syntax, relational semantics,
    • models and frames,
    • bisimulations, van Benthem’s bisimulation characterisation theorem,
    • first-order correspondence, Sahlqvist algorithm,
    • model-theoretic and frame-theoretic constructions,
    • soundness and completeness, the finite model property
  • Recommended prior knowledge: Knowledge of propositional logic and first order logic (syntax and semantics).
  • Format: Weekly lectures.
  • Study materials: Modal Logic, Blackburn, de Rijke, Venema, Cambridge University Press, 2001.
  • Additional literature
  • Alexander Chagrov and Michael Zakharyaschev: Modal Logic, Oxford University Press, 1997.
  • Johan van Benthem : Modal Logic for Open Minds, 2010.
  • Marcus Kracht: Tools and Techniques in Modal Logic, Elsevier, 1999.
  • Dov M. Gabbay, A. Kurucz, F. Wolter, M. Zakharyaschev: Many-Dimensional Modal Logics: Theory and Applications, Elsevier, 2003.