Neighborhood Semantics for Modal Logic

Lecturer: Eric Pacuit (website)
Location: ILLC, F1.15

Course Description

Neighborhood models are generalizations of the standard relational models for modal logic invented independently by Dana Scott and Richard Montague in 1970. Neighborhood models provide simple semantics for many interesting non-normal modalities. A general criticism of neighborhood models is that they are not well-motivated. They do provide a semantics for weak systems of modal logic, but do they do so in a principled way? There is certainly some truth to this criticism. Nonetheless, recent work has demonstrated the usefulness and interest of neighborhood semantics. Neighborhood structures naturally show up when studying cooperative and non-cooperative game theory. Furthermore, neighborhood semantics can be given an epistemic interpretation as the evidence that an agent has accepted at a given state. Finally, one can learn something about normal systems of modal logic by looking at how these systems behave in a more general semantics. This course will introduce the basic techniques and results of neighborhood semantics for modal logic and explain the exact relationship between the standard relational models, neighborhood models and topological models for modal logics. The main objective is to demonstrate precisely where neighborhood models fit within the large family of semantic frameworks for modal logic and discuss both the pitfalls and potential uses of these very general structures. The course will be based on a new book "Neighborhood Semantics for Modal Logic" by the instructor, but background material of current research papers will also be discussed.

Course description on the ILLC website.

Requirments

You may either solve some problems from the book or write a paper. Please email me your solutions/paper no later than July 25, 2016. Good Luck!

Course description on the ILLC website.

Lecture 1: Introduction and Motivation I

Slides

Date: Wednesday, June 1, 14:00-16:00

Reading: Chapter 1, Neighborhood Semantics for Modal Logic

Lecture 2: Introduction and Motivation II

Slides

Date: Thursday, June 2, 12:30-14:30

Reading: Chapter 1, Neighborhood Semantics for Modal Logic

Lecture 3: Core Theory (Completeness, Bisimulations, Alternative Semantics)

Slides

Date: Tuesday, June 7, 14:00-16:00

Reading: Chapter 2, Neighborhood Semantics for Modal Logic

Lectures 4 & 5: Advanced Topics (Incompleteness, Standard Translation, Model Theory)

Slides - Lecture 4
Slides - Lecture 5

Date: Wednesday, June 8, 11:00-13:00 and 14:00-16:00

Reading: Chapter 2, Neighborhood Semantics for Modal Logic

Lecture 6: Richer Languages (Universal Modality, Nominals, First-Order Extensions)

Slides

Date: Thursday, June 9, 12:30-14:30

Reading: Chapter 3, Neighborhood Semantics for Modal Logic

Lecture 7: Richer Languages (First-Order Extensions, Game Logic, Common Belief)

Slides

Date: Monday, June 13, 12:30-15:00

Reading: Chapter 3, Neighborhood Semantics for Modal Logic

Lecture 8: Richer Languages (Common Belief, Dynamic Extensions)

Slides

Date: Tuesday, June 14, 11:00-13:00

Reading: Chapter 3, Neighborhood Semantics for Modal Logic

Final Meeting (Make-Up, Presentations, Concluding Remarks)



Date: Wednesday, June 15, 10:00-12:00

Reading: Chapters 1, 2, 3, Appendix A