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Modal logic is an extension of ordinary, "classical" logic which allows formalizations (for instance) of phrases such as "it is possible that" and "it is necessary that" (the alethic modalities). Modal logics have important applications in philosophy, but also in linguistics and computer science. The course will provide an introduction to the basics of modal logics, especially their semantics, and will also cover various specific systems and their applications - the particular choice of topics will depend on the interests of the class. We will cover the alethic modalities, and also study logics of belief and knowledge, of time, of obligation, combinations thereof (e.g., dynamic epistemic logic), as well as related topics such as logics of counterfactual conditionals and intuitionistic logic.

Phil 279 (Logic I) is a prerequisite for this course.

We will use the following book as a guide:

- Johan van Benthem,
*Modal Logic for Open Minds*. (CSLI Publications, 2010)

The following are useful references:

- Patrick Blackburn, Johan Van Benthem and Frank Wolter,
*Handbook of Modal Logic*(Elsevier, 2007) -- available online. - Patrick Blackburn, Maarten de Rijke, Yde Venema,
*Modal Logic*(Cambridge University Press, 2002) - James Garson, Modal Logic for Philosophers (Cambridge University Press, 2006)

Three homework assignments (60%, 20% each) and a final paper (30%) are required to pass the course. There will be no exams. You will give a short presentation on the topic of your final project in the last week of; this presentation will make up 5% of your grade. The remaining 5% will be based on participation in discussion in-class and on the course website.

The final project will consist in either a worked out presentation of an advanced topic (e.g., a proof of a theorem in the metatheory of modal logic, a survey article on some application of modal logic in computer science, logic, or linguistics), or a philosophical paper on a topic related to modal logic. A technical project should run about 7-10 pages; a more philosophical paper 10-15 pages. You will give a short presentation on your project/paper (10-20 minutes, depending on class size) in the last week of class. Technical projects may be completed in groups of up to

3 students. If done in a team, the paper should be 10-15 pages long, and the presentation 20-30 minutes shared between team members.

Assignments handed in late will be penalized by the equivalent of one grade point per calendar day.

Collaboration on exercises is encouraged. However, you must write up your own solutions, and obviously you must not simply copy someone else’s solutions. You are also required to list the names of the students with whom you’ve collaborated on the assignment.

Graduate students registered in Phil 679.5 will be expected to complete all the above requirements. Graduate students will be expected to choose more advanced final project topics. Graduate student papers should run 15–20 pages. Collaboration on final projects is allowed, but every graduate student must submit a distinct, self-contained paper, and give a self-contained presentation.

- Introduction. Modal languages. Possible worlds. Sets and relations. Basics of relational semantics
- Frames and models. The forcing relation. Validity and consequence. Proving formulas valid, constructing counterexamples.
- Basic model theory: Bisimulations. Generated submodels. Unraveling.
- Axiom systems for normal modal logics. Deductions. Soundness.
- Canonical models and completeness.
- Finite model property and decidability
- Proof systems for modal logics
- Translations and frame correspondence
- First-order modal logic.
- Applications, covering some of:
- Doxastic and epistemic logic (logics of belief and knowledge)
- Dynamic logic (logics of actions and change)
- Logics of time
- Conditional logics
- Intuitionistic logic

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