Basic Concepts in Modal Logic

Philosophy 169

Spring 1990


Edward N. Zalta, Philosophy Department
Offices: Cordura 226 (CSLI) and 92EE (Philosophy)
Phone: 723-0345 (Cordura), 723-2192 (92EE)
Electronic Mail: zalta@csli
Mailboxes: Building 90 Lounge and Ventura Hall
Office Hours: At Cordura: Wednesday, 3 - 4:30, and by appointment

Class Meetings:

Lectures: Tuesday, Thursday, 1:15 - 2:30 P.M., Esmb (Mitchell) 138 Weekly `working' section, depending on class size and TA availability

Course Description:

In this class we examine the structural similarities among (the models of) various modal logics. It is customary in philosophy to call the following propositional operators `modalities': it is metaphysically necessary (possible) that, it is physically necessary that, it is known (believed) by person S that, it will be (was) the case that, it ought to be the case that, and after every (some) terminating execution of the program alpha, it is the case that. These operators are called `modalities' because when they are appled to a proposition p, the proposition that results, for example, it is necessary that p, expresses some way or mode in which p is true. So modal logic is the study of the valid patterns of reasoning with respect to each modality and why it is that the rules of inference that legitimize such patterns never allow us to infer (modal) falsehoods from (modal) truths. We shall see how these `logics' of modality have been unified in a rather interesting way.

Required Texts:

Resource Texts:

Course Prerequisite:

Philosophy 159 - You will have better perspective on things in general if you have had 160A, but with 4 units worth of effort, students with a 159 background should be able to come to a reasonably deep understanding of the material.

Class Requirements

  1. 5 Problem Sets. As a group, the problem sets are worth 45%of your grade.
  2. MIDTERM EXAM (May 1): The midterm is worth 25%of your grade.
  3. FINAL EXAM (June 12): The final is worth 30%of your grade.


NOTE: The pace at which the material will be presented will depend on the background of the students. Consequently, the following schedule is tentative and subject to change. Reading assignments, and exercise assignments, will be announced in class.


3 - Introduction to Modality
5 - A Modal Language
10 - Models for the Language
12 - Other Valid and Invalid Formulas
17 - Validity with respect to a Class of Models
19 - Preserving Validity and Truth; Rules of Inference
24 - Modal Logics and Theoremhood
26 - Deducibility, Consistent Sets and Maximal Consistent Sets


3 - Normal Modal Logics
8 - Normal Logics and Maximal Consistent Sets
10 - Soundness of Modal Systems
15 - Canonical Models
17 - Completeness of Modal Systems
22 - Modal Predicate Logic: Language and Kripke Models
24 - Barcan Formulas
29 - Formulas Invalid in Kripke's Systems

31 - Other Applications of Modal Logic


5 - Dead Week


1. Midterm: May 1

2. Final: Tuesday evening, June 12, 7:00 - 10:00 PM


1. Exercises are due at the beginning of class on the day they are assigned as due. Exercise sets turned in after that time are counted as late, and will be assessed, roughly, a 25%per diem penalty (if you suppose that 100 points can be earned in the course, and that each exercise set is therefore worth 9 points, then the penalty for a late exercise is two points per day).

2. No make-up exams or incompletes will be given, unless there is a genuine emergency or the circumstances are exceptional in some other way.

3. Reevaluations: Students may request a reevaluation of an exercise or exam problem if they feel that it has been incorrectly graded. The work must be resubmitted to the professor within one week of the date the problem was graded and returned.

Copyright © 1994, by Edward N. Zalta. All rights reserved.