Logic 2: Modal Logic (Autumn 2019)
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.
Dr Wolfgang Schwarz (firstname.lastname@example.org)
Office hour: Thursday 15:00-16:00 and by appointment
My office is room 6.02, Dugald Stewart Building.
Ann-Marie Cowe (email@example.com)
Lecture notes with exercises will be made available each week, and are the only required reading.
If you want to look ahead, here are the notes from last year (PDF). The content will change for this year, however, so pay attention to what I upload to the syllabus below!
You are encouraged (but not required) to work through the following textbook alongside the classes:
- Rod Girle, Modal Logics and Philosophy, 2nd edition, 2009
If you want to know even more, get one (or both) of these:
- Graham Priest, An Introduction to Non-Classical Logic, 2nd edition, 2008
- G.E. Hughes and Max Cresswell, A New Introduction to Modal Logic, 1996
- Lecture 1: Monday 10:00-10:50, Room G.06, 50 George Square
- Lecture 2: Wednesday 10:00-10:50, Room S.1, 7 George Square
- Tutorial Group 1: Tuesday 11:10-13:00, Room 1.20, DSB
- Tutorial Group 2: Monday 14:10-16:00, Room 4.2, Lister Learning and Teaching Centre, 5 Roxburgh Place
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.
In addition to the final exam, which accounts for 50% of the grade, there will be two take-home tests, the first counting 20%, the second 30%.
The first take-home test will be released on Monday 7th October, and is due by Thursday 10th October.
The second take-home test will be released on Monday 4th November, and is due by Thursday 7th November.
The final exam will take place in December. The precise date and location are not yet known.
Week 1: Modal Operators
The language of modal propositional logic. Reasoning about necessity and possibility. Flavours of modality. Some branches of modal logic.
Week 2: Possible Worlds
Basic possible-worlds semantics for modal propositional logic. Tree rules to establish validity and find counterexamples.
Week 3: Accessibility
Adding an accessibility relation to possible-worlds models. Properties of the accessibility relation and corresponding logical systems.
Week 4: Proofs
Natural deduction systems and axiomatic systems. Soundness and completeness. 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'. Two-dimensional modal logics.
Week 8: Conditionals
The ``paradoxes of material implication''. Strict implication. Lewis-Stalnaker conditionals. If-clauses as restrictors.
Week 9: Modal Predicate Logic
Modality de dicto and de re. Predicate logic recap. Predicate logic as a modal logic. Challenges for a modal predicate logic.
Week 10: Existence
The connection between quantification and existence. Constant domain models and variable domain models. Free logics.
Week 11: Trans-World Identity
Rigid and non-rigid designators. Contingent identity. Counterpart models.