Logic and Philosophy of Science Seminar

Modal Logic


The final problem set is available here. Please hand in solutions by Tuesday, May 22, 2012.

Instructor: Eric Pacuit
Office Hours: Thursdays, 2:00 PM - 3:00 PM
Office Location: 1103A Skinner Building
Meeting Times: Tuesdays, 6:00PM - 8:30PM
Course Number: PHIL 858A
Semester: Spring 2012
First Class: Tuesday, January 31, 2012
Location: Skinner 1116

Course Contents

Modal logic began as the study of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), temporal (“it has been the case that”), among others. (See Roberta Ballarin's article in the Stanford Encyclopedia of Philosophy for the "modern origins" of modal logic.) By now, it has become a broad area of research, forming a sort of lingua franca between many disciplines, especially philosophy, computer science, economics, and linguistics.

There are two main goals in this course. The first goal is to introduce the basic techniques and concepts in modal logic. We will focus on the basic systems of modal logic (both propositional and predicate) and their metatheory (e.g., issues of completeness/incompleteness, decidability, and definability). The second goal is to critically examine the many variations and philosophical interpretations of the basic systems of modal logic. Topics that may be discussed (the final choice of topics will depend on student interest) include (dynamic) epistemic/doxastic logic, conditional logic, non-normal modal logics, logics of action and agency, applications of modal logic in game theory, intuitionistic logic, among others.

Students will come away from this course with a working knowledge of modal logic and its use in philosophy, computer science and game theory. The main objective is that students should be able to confidently apply techniques from modal logic to problems in their area of research. They should be able to apply existing modal logics where appropriate and design new logical systems when necessary, and rigorously analyze their properties.

Related Courses. For more information about the topics which may be discussed during the semester, you can consult the webpages of the following related courses that I have taught:
  • Logic and Artificial Intelligence, Advanced undergraduate/graduate course focusing on (dynamic) epsitemic logic, belief revision and preference logic taught at the Department of Philosophy at Carnegie Mellon University.
  • Logics of Rational Agency, Short course taught at the North American Summer School for Logic, Language and Information (NASSLLI 2010). Also, see the earlier version taught at the European Summer School for Logic, Language and Information (ESSLLI 2009).
  • Introduction to Modal Logic, Introductory course on modal for Masters of Logic students at the Institute for Logic, Language and Information, University of Amsterdam.

Reading Material

The main textbook for the course will be:

  • [MLOM] Johan van Benthem (2010). Modal Logic for Open Minds, CSLI Publications.

  • In addition, the following books and survey articles are recommended (the relevant excerpts will be made available in class):

    Below is a list of some general surveys and textbooks covering applications and variations of the basic modal systems. This is not a complete list of all relevant material, but a reasonably large sampling. Consult the schedule for the specific papers and excerpts from the books below that we will discuss in class.

    • First-order modal logic
    • (Dynamic) logics of knowledge and belief
      • Johan van Benthem (2011). Logical Dynamics of Information and Interaction, Cambridge University Press. (This will be available only in September, I will hand out versions of his chapters as needed.)
      • Eric Pacuit (2011). "Dynamic Epistemic Logic", forthcoming in Philosophy Compass.
      • R. Fagin, J. Halpern, Y. Moses and M. Vardi (1995). Reasoning About Knowledge , The MIT Press.
    • The logic of conditionals
      • Horacio Arlo-Costa, "The Logic of Conditionals", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.).
    • Modal logics of preference
    • Logics of action, agency and ability
      • Krister Segerberg, John-Jules Meyer, and Marcus Kracht, "The Logic of Action", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.).
      • Y. Shoham (2009). "Logical Theories of Intention and the Database Perspective," Journal of Philosophical Logic, 38(6): 633-648. (PDF)
    • Modal logic and game theory
      • Johan van Benthem, Eric Pacuit and Olivier Roy (2011). "Games and Interaction: the Logical Perspective," Games, 2(1): 52 - 86. (PDF)


Please consult this schedule regularly throughout the semester as meeting times and readings may change.

1/31 Introductory Remarks (slides) Chapter 1 & 2 of [MLOM]
HW: Problems 1 and 2 on pg. 23
2/7 Model Constructions and Bisimulations (handout) Chapter 3 of [MLOM]
2/14 Bisimulation Games (handout) Chapter 3 of [MLOM]
Model Theory of Modal Logic, Section 3.1
2/21 Class Canceled (we will reschedule)
2/28 Ultrafilter Extensions, Standard Translation, Finite Tree Property (Proofs discussed in class) Chapters 4 & 7 of [MLOM]
Problem Set 1
3/6 The Finite Model Property, The Landscape of Modal Logics (handout)
Modal deduction examples
Chapters 4, 5, & 8 of [MLOM]
Problem Set 1 Due
3/13 Completeness of Normal Modal Logic (handout) Chapter 5 & 8 of [MLOM]
Problem Set 2
3/20 Spring Break: No Class
3/27 Correspondence Theory (handout) Chapter 9 & 10 [MLOM]
Problem Set 2 Due
4/3 Incompleteness and General Frames (handout) Chapter 26 of [MLOM]
4/10 Application: Logics of Knowledge and Belief (slides)
(Survey on Logics of Knowledge and Belief)
Chapters 12 & 13 of [MLOM]
4/17 Application: Common Knowledge, Agreeing to Disagree (slides)
Chapter 12 & 13 of [MLOM]
D. Samet, Agreeing to disagree: The non-probabilistic case, Games and Economic Behavior, 2010.
4/24 Application: Dynamics of Knowledge and Belief (slides)
(Survey on Dynamic Logics of Knowledge and Belief)
Chapter 15 of [MLOM]
R. Stalnaker, Iterated Belief Revision, Erkenntnis, 2009
5/1 Modal Preference Logics (slides)
D. Osherson and S. Weinstein, Preferences based on reasons
Chapter 17 of [MLOM]
Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences, Journal of Philosophical Logic, 38:1, 2009.
5/8 First-order Extensions
M. Fitting, First Order Intensional Logic, APAL, 2004
Chapter 11 & 27 of [MLOM]
Chapter 4 of First-Order Modal Logic by Fitting and Mendelsohn (handed out in class)

Problem Set 3 Due
5/14 Make-up class: 10:30 AM - 12:00 AM
Conclusions and Modal Foundations of Classical Logic
Chapter 27 of [MLOM]


Students who want credit for the course must:
  1. Turn in assigned problem sets, which will be nuts and bolts, nothing tricky. Their main function, in fact, is to show me how well you are understanding the material. Problem Set 1, Problem Set 2, Problem Set 3, Final Problem Set