Modal Logic

General information

• Seminars: Mondays 12:00—14:00, Room 021, Ludwigstr. 31.
• Problem classes: Thursdays 14:00—15:00, Room D 102, Richard-Wagner-Str. 10.
• Language: English.
• Prerequisites: Familiarity with the fundamentals of propositional and predicate calculus is required. Knowledge of standard metalogical results (soundness, completeness) is desirable but not required.
• Lecturer:
  • Benedict Eastaugh (benedict.eastaugh@lrz.uni-muenchen.de).
  • Office: Room 123, Ludwigstr. 31.
  • Office hours: Mondays 15:00—17:00, or by appointment.

Course description

It is possible that it will rain tomorrow; it is necessary that you are identical to yourself; I believe that the sky is green; it is obligatory to laugh at your logic teacher’s jokes. These sentences are all examples of modal judgements: assertions involving the use of modals like ‘possible’, ’necessary’, ‘believe’, and ‘obligatory’. Modal judgements have been studied through the lens of logic since antiquity, and modal logic experienced a renaissance in the second half of the 20th century, sparked by the introduction of possible worlds semantics, where modal operators like “it is necessary that” and “it is possible that” are interpreted as quantifying over possible worlds or states of affairs. This course will introduce you to the fundamentals of classical propositional and quantified modal logic. We will study proof systems and possible world semantics for different modal logics, and see how the formal regimentation of modality allows us to make precise (and sometimes helps us resolve) philosophical puzzles concerning existence, identity, and reference.

Content and readings

For details, see the schedule below.

The essential readings for the course will largely be drawn from the textbook First-Order Modal Logic [Fitting and Mendelsohn 1998]. The first half of the course will be concerned with classical propositional modal logic, including: possible worlds (Kripke) semantics; tableau and Hilbert proof systems; the main propositional modal logics such as K, T, S4, and S5; and soundness and completeness theorems for these logics. In the second half of the course we will look at quantified modal logic.

Each week has a list of required readings, which will be necessary to follow the course. I have also supplied a list of supplementary readings, which complement or augment the primary material for that week, either by providing historical or philosophical background; by providing an alternative view on the technical material; or by providing additional material which goes beyond that required for the course, so that you can start to learn further topics by yourself.

In addition to the readings, every Monday there will be a list of exercises for you to complete. We will then go through them (and possibly others) in the problem classes on Thursdays.

Assessment

The course will be assessed by means of a final take-home exam.

Schedule

Bibliography

• Blackburn, P., M. de Rijke, and Y. Venema (2001). Modal Logic. Cambridge University Press.
• Blackburn, P., J. van Bentham, and F. Wolter, eds. (2007). Handbook of Modal Logic. Elsevier.
• Fitting, M. and R. L. Mendelsohn (1998). First-Order Modal Logic. Springer.
• Garson, J. W. (2013). Modal Logic for Philosophers. Cambridge University Press.
• Garson, J. (2018). Modal Logic. In E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2018 Edition). [link]
• Linnebo, Ø. and Shapiro, S. (2019). Actual and potential infinity. Noûs 53(1):160–191. [link]
• Zach, R. et al (2018). Boxes and Diamonds: An Open Introduction to Modal Logic. Open Logic Project. [link]