An Introduction to Modal Logic

Instructor: Churn-Jung Liau

This lecture covers basic modal logic and its applications (in particular, in AI and distributed systems). Specific topics include: Kripke semantics, normal modal systems (K, D, S5, etc.), completeness theorem, finite model property, decidability, multi-agent epistemic logic, dynamic logic.

Prerequisites

Elementary Logic

Syllabus

basic modal logic: syntax, Kripke semantics, model-theoretic notions
normal systems of modal logic: K, D, T, S4, S5, etc.
meta-theorems of normal systems: soundness, completeness, decidability
generalization of basic modal logic: multi-dimensional and multimodal logic
multi-agent epistemic logic
dynamic logic

Course Materials

Homework Assignment

Homework 1 [Homework(PDF)] [Solutions] (Due: 9:00am in class, Friday, 07/03/2009)
Homework 2 [Homework(PDF)] [Solutions] (Due: 9:00am in class, Monday, 07/06/2009)
Homework 3 [Homework(PDF)] [Solutions] (Due: 9:00am in class, Monday, 07/06/2009)

References

Books

B.F. Chellas. Modal Logic: An Introduction. Cambridge University Press, 1980.
P. Blackburn, M. De Rijke, and Y. Venema. Modal Logic. Cambridge University Press, 2001.
R. Fagin, J.Y. Halpern, Y. Moses, and M.Y. Vardi. Reasoning about Knowledge. The MIT Press, 1995.
D. Harel, D. Kozen, and J. Tiuryn. Dynamic Logic. The MIT Press, 2000.
G. Hughes and M.J. Cresswell. A Companion to Modal Logic. Methuen, 1984.
G. Hughes and M.J. Cresswell. A New Introduction to Modal Logic. Routledge, 1996.
A. Chagrov and M. Zakharyaschev. Modal logic. Oxford University Press, 1997.
N.B. Cocchiarella and M.A. Freund. Modal Logic: An Introduction to its Syntax and Semantics. Oxford University Press, 2008.

Handbooks

P. Blackburn, J. van Benthem, and F. Wolter. Handbook of Modal Logic. Elsevier, 2007.
F. Baader, D. Calvanese, D. McGuinness, D. Nardi, and P. Patel-Schneider. The Description Logic Handbook. Cambridge University Press, 2003
D.M. Gabbay and F. Guenthner. Handbook of Philosophical Logic, Vol 3. Springer, 2001.
D.M. Gabbay and F. Guenthner. Handbook of Philosophical Logic, Vol 4, 7, and 8. Springer, 2002.
D.M. Gabbay and F. Guenthner. Handbook of Philosophical Logic, Vol 10 and 11. Springer, 2004.
D.M. Gabbay and F. Guenthner. Handbook of Philosophical Logic, Vol 13. Springer, 2005.
D.M. Gabbay and F. Guenthner. Handbook of Philosophical Logic, Vol 14. Springer, 2007.
S. Abramsky, D.M. Gabbay, and T. Maibaum. Handbook of Logic in Computer Science, Vol 2. Oxford University Press, 1992.
D.M. Gabbay, C. Hogger, and J.A. Robinson. Handbook of Logic in Artificial Intelligence and Logic Programming, Vol 4. Oxford University Press, 1995.
D.M. Gabbay and J. Woods. Handbook of the History of Logic, Vol 7: Logic and the Modalities in the Twentieth Century. Elsevier, 2006.
M. Aiello, I. Pratt-Hartmann, and J. van Benthem. Handbook of Spatial Logics. Springer, 2007.
J. van Leeuwen. Handbook of Theoretical Computer Science, Vol B. Elsevier, 1990.

Internet resources