Modal Logic

Practical information

Mondays, from 2pm to 4pm

Practice sessions: Mondays, from 6pm to 7pm

Office hours by appointment, in room 234, Ludwigstrasse 31, second floor

You can find the take-home exam here. You can either take it or write an essay (ca 15 pages). In both cases, the deadline is September 22, 2017. Please send me your answers/essay per email. We can discuss topics if you need advice wrt the essay. I can also recommend bibliography. If something is unclear or you are having serious trouble with some of the exercises, drop me an email.

You can find the text book here (credits to Max).

Here's a cool tool for drawing Kripke-models!


0. Introduction: What is Modal Logic?


Read: Garson's (2013), Introduction: What is Modal Logic?

1. System K: Language and Natural Deduction


Read: Garson's (2013), Chapter 1, except section 1.6.

Exercises: all exercises in the chapter except those in section 1.6 and exercise 1.14.

2. Extensions of K

15/5 - 29/5

Read: Garson's (2013), Chapter 2, except sections 2.2 and 2.8.

Exercises: all exercises in the chapter before section 2.8. For exercises 2.2 and 2.16, don't write an essay (if you don't feel like it), just consider the questions.

3. Possible-Worlds Semantics


Read: Garson's (2013), Chapter 3.

Exercises: all exercises in the chapter expect exercise 3.3.a) and 3.4.c).

4. The Accessibility Relation


Read: Garson's (2013), Chapter 5, except sec. 5.5.

Exercises: 1, 2, 4, 5, 6, 13.

5. Soundness and Completeness for Modal Propositional Systems

19/6 - 26/6

Read: Garson's (2013), Chapter 9.

6. How to Introduce Quantifiers to Modal Logic?

A) The Failure of Leibniz Law

3/7 - 10/7

Read: Garson's (2013), Chapter 12.1-3; Russell's (1905) "On Denoting".

B) The Problem of Non-Denoting Terms

10/7 - 17/7

Read: Garson's (2013), Chapter 12.4; Quine's (1963) "On What there is"; Nelson's (2012) "Existence".

C) Constant vs Variable Domains - Rigid and Non-Rigid Designators

17/7 - 24/7

Read: Garson's (2013), Chapter 12.7-13; Linsky and Zalta's (1994) "In Defense of the Simplest Quantified Modal Logic"; Kripke's (1963) "Semantical Considerations in Modal Logic".

Exercises: all in the chapter except 12.19-22.

7. Semantics for Quantified Modal Logics


Read: Garson's (2013), Chapter 13.1-5.

Exercises: 13.2, 8, 9, and 10.

Course description

The course consists in a thorough introduction to modal logic. Modal logics are mainly concerned with the deductive behaviour of modalities. These are primarily the alethic modalities (ways in which a sentence can be true) ‘it is necessary that’ or ‘necessarily’ and ‘it is possible that’ or ‘possibly’, but also include epistemic modalities such as ‘is known that’ and ‘is believed that’, deontic modalities such as ‘it is obligatory that’ and ‘it is permitted that’, tense modalities, and provability modalities, among others.

The first half of the course is devoted to modal propositional logics, their semantics and proof-theory, as well as the presentation of well-known metatheoretic results. This includes a detailed exposition of possible-worlds semantics, an tool ubiquitous tool in mathematical philosophy. The second half of the course focuses on modal predicate logics, their semantics, proof-theory and salient metatheoretic results. Students are introduced to the traditional philosophical issues revolving around the identity relation, predicates of existence, definite descriptions, Barcan formulae, and intensional objects.

Course material

  • Lecture notes
  • Garson's Modal Logic for Philosophers


  • Barcan (Marcus), R. 1967 “Essentialism in Modal Logic,” Noûs, 1: 91-96.
  • Bencivenga, E., 1986, “Free Logics,” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, III.6, Dordrecht: D. Reidel, 373-426.
  • Blackburn, P., with M. de Rijke and Y. Venema, 2001, Modal Logic, Cambridge: Cambridge University Press.
  • Blackburn, P., with J. van Bentham and F. Wolter, 2007, Handbook of Modal Logic, Amsterdam: Elsevier.
  • Bull, R. and K. Segerberg, 1984, “Basic Modal Logic,” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, II.1, Dordrecht: D. Reidel, 1-88.
  • Carnap, R., 1947, Meaning and Necessity, Chicago: U. Chicago Press.
  • Chagrov, A. and M. Zakharyaschev, 1997, Modal Logic, Oxford: Oxford University Press.
  • Chellas, B., 1980, Modal Logic: An Introduction, Cambridge: Cambridge University Press.
  • Cresswell, M. J., 2001, “Modal Logic”, in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Oxford: Blackwell, 136-158.
  • –––, 1991, “In Defence of the Barcan Formula,” Logique et Analyse, 135-136: 271-282.
  • –––, 1995, “Incompleteness and the Barcan formula”, Journal of Philosophical Logic, 24: 379-403.
  • Cocchiarella, N. and M. Freund, 2008, Modal Logic An Introduction to its Syntax and Semantics, New York: Oxford.
  • Fitting, M. and R. Mendelsohn, 1998, First Order Modal Logic, Dordrecht: Kluwer.
  • Garson, J., 2001, “Quantification in Modal Logic,” in D. Gabbay and F. Guenthner (eds.) Handbook of Philosophical Logic, second edition, volume 3, Dordrecht: D. Reidel, 267-323.
  • –––, 2005, “Unifying Quantified Modal Logic,” Journal of Philosophical Logic, 34: 621-649.
  • –––, 2013, Modal Logic for Philosophers, Second Edition, Cambridge: Cambridge University Press.
  • Hughes, G. & Cresswell, M. (1996), A New Introduction to Modal Logic, Routledge.
  • Kaplan, D., 1989, “Demonstratives”, in Themes from Kaplan, Oxford: Oxford University Press.
  • Kripke, S., 1963, “Semantical Considerations on Modal Logic,” Acta Philosophica Fennica, 16: 83-94.
  • –––, 1980, Naming and Necessity, Cambridge, MA: Harvard University Press.
  • Konyndik, K., 1986, Introductory Modal Logic, Notre Dame: University of Notre Dame Press.
  • Lemmon, E. and D. Scott, 1977, An Introduction to Modal Logic, Oxford: Blackwell.
  • Linsky, B. and E. Zalta, 1994, “In Defense of the Simplest Quantified Modal Logic,” Philosophical Perspectives, (Logic and Language), 8: 431-458.
  • Mints, G. 1992, A Short Introduction to Modal Logic, Chicago: University of Chicago Press.
  • Nelson, M. (2012) "Existence", The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = <>.
  • Ponse, A., with M. de Rijke, and Y. Venema, 1995, Modal Logic and Process Algebra, A Bisimulation Perspective, Stanford: CSLI Publications.
  • Popkorn, S., 1995, First Steps in Modal Logic, Cambridge: Cambridge University Press.
  • Quine, W. V. O., 1953, “Reference and Modality”, in From a Logical Point of View, Cambridge, MA: Harvard University Press. 139-159.
  • ---, 1963, "On What There Is," in From a Logical Point of View, Harper & Row, chapter 1, 1-19.
  • Russell, B. 1905, "On Denoting", Mind 14: 479-493.
  • Zeman, J., 1973, Modal Logic, The Lewis-Modal Systems, Oxford: Oxford University Press.