Modal Logic (Phil 513/679)

Official outlines at the end of this page.

Contents

• Instructor
• Lectures
• Course description
• Required Textbook
• Evaluation
• Assignments and Policies
• Course Website

Course Description

Modal logic is an extension of ordinary, “classical” logic which allows formalizations 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 basic systems of modal logic, both propositional and predicate, their metatheory, philosophical interpretation, and applications. We will concentrate on the alethic modalities, but also study logics of belief and knowledge, of time, of obligation, and intuitionistic logic

Prerequisites

Phil 279 (Logic I) is a prerequisite for this course. Phil 379 (Logic II) is recommended, but not necessary.

Recommended Texts

There is no required text. The following are useful references, however:

Patrick Blackburn, Maarten de Rijke, Yde Venema, Modal Logic (Cambridge University Press, 2002)

Rod Girle, Modal Logics and Philosophy (McGill-Queen's University Press, 2000)

Evaluation

Three homework assignments (45%, 15% each), a final project (30%), an in-class presentation (5%), and class participation (20%).

Assignments and Policies

Late work and extensions

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

Collaboration

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.

Final Project

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), or a paper linking modal logic with philosophical topics in modality. A technical project should run about 7–10 pages; a more philosophical paper 10–15 pages. Technical projects may be completed in groups of up to 3 students.

You will give a short presentation on your project/paper (10 minutes) in the last week of class.

Requirements for Graduate Students

Graduate students registered in Phil 679.05 will be expected to complete all the above requirements. Assignments for graduate students will contain harder problems, and will have to choose more advanced final project topics. If a philosophical topic is chosen for the final paper, it should run 15–20 pages.

Course Website

A course website on U of C's BlackBoard server has been set up. You will be automatically registered if you're registered in the class. To access the BlackBoard site, you can either go directly to blackboard.ucalgary.ca and log in with your UCIT account name and password, or you can access it through the myUofC portal (my.ucalgary.ca; log in with your eID). If you don't have an eID or UCIT account, see elearn.ucalgary.ca/help.html.

Topics

1. Introduction. Modal languages.  Possible worlds.  Sets and relations. Basics of relational semantics
2. Frames and  models.  The forcing relation. Validity and consequence.  Proving formulas valid, constructing counterexamples. Frame definability.
3. Axiom systems for normal modal logics. Deductions. Soundness.
4. Generated submodels. Bisimulations. Canonical models and completeness.
5. Epistemic logic.

Official Outlines