Logic 2: Modal Logic

This is a follow-on course to Logic 1, focusing on modal extensions of classical propositional and predicate logic.

Modal logic is used to reason about possibility and necessity, knowledge and belief, permission and obligation, past and future, and a variety of other topics. The first part of the course will introduce standard models and proofs for propositional modal logic, with a brief look at the meta-logical properties of soundness and completeness. We will then go through a range of philosophical applications, studying the logic of knowledge, the logic of obligation, the logic of time, and logical properties of "if-then" constructions. Finally, we will turn to quantified modal logic. We will look at the choices between constant and variable domains, rigid and non-rigid names, and discuss whether standard predicate logic should be weakened to a "free" logic.

Course organiser

Dr Wolfgang Schwarz (wolfgang.schwarz@ed.ac.uk)

Office hours: Friday 12:00-13:00 and by appointment

My office is room 8.06, 40 George Square.

Course Secretary

James Donaldson (philinfo@ed.ac.uk)

Classes

Lectures:

Thursday 13:10-14:00, Dugald Stewart Building, room 1.20
Friday 13:10-14:00, Dugald Stewart Building, room 1.20

Tutorials:

Group 1: Tuesday 11:10-13:00 Lister Learning and Teaching Centre, room 2.2
Group 2: Wednesday 16:10-18:00 Lister Learning and Teaching Centre, room 2.2

Tutorials start in week 2. Only the first hour of tutorials is compulsory.

If you'd like to change your tutorial group, please use the "Group Change Request form" on the timetabling website.

Assessment

First take-home test (20%), release TBC
Second take-home test (30%), release TBC
Final exam (50%), date and location TBC

Readings

Lecture notes with exercises can be found here in HTML format or here in PDF. They are the only required reading.

If you want to get a wider perspective or further help, you may find one or more of the following books useful (listed with increasing difficulty):

Rod Girle, Modal Logics and Philosophy, 2nd edition, 2009
Graham Priest, An Introduction to Non-Classical Logic, 2nd edition, 2008
G.E. Hughes and Max Cresswell, A New Introduction to Modal Logic, 1996

Syllabus

Week 1: Modal Operators

The language of modal propositional logic. Reasoning about necessity and possibility. Flavours of modality. Axiomatic systems.

Week 2: Possible Worlds

Basic possible-worlds semantics for modal propositional logic. The tree method for establishing validity and finding counterexamples.

Week 3: Accessibility

Adding an accessibility relation to possible-worlds models. Properties of the accessibility relation and corresponding axioms.

Optional bonus text: Natural deduction proofs (PDF)

Week 4: Models and Proofs

Soundness and completeness for trees and the axiomatic method. A brief look at the logic of provability.

Week 5: Epistemic Logic

The logics of knowledge and belief. Gaining information as excluding possibilities. Modal logics with multiple modalities. Interaction principles.

Week 6: Deontic Logic

The logic of obligation and permission. Ideal-worlds models. Some puzzles and paradoxes. Neighbourhood models. The concept of conditional obligation.

Week 7: Temporal Logic

The logic of past, present, and future. Worlds and times. Branching time. `Now'.

Week 8: Conditionals

Material conditionals. Strict conditionals. Variably strict conditionals. If-clauses as restrictors.

Week 9: Towards Modal Predicate Logic

Predicate logic recap. Modal fragments of predicate logic. Modality de dicto and de re. Identity and descriptions.

Week 10: Semantics for Modal Predicate Logic

Constant domain semantics and variable domain semantics. Quantification and existence. Trans-world identity.