2nd Semester 2015/16: Neighborhood Semantics for Modal Logic

Instructor: Eric Pacuit (University of Maryland). [The project is coordinated at the ILLC by Sonja Smets]
If you are interested in this project, please contact the instructor by email.

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.

Organisation: There will be 8 sessions of two hours on 1, 2, 7, 8, 9, 13, 14, 15 June. The schedule includes additional time for student presentations.

Schedule: 1. Introduction and Background on Modal Logic 2. Introduction to Neighborhood Semantics 3. Core Theory I 4. Core Theory II 5. Advanced Topics 6. Richer Languages: Universal Modalities and Nominals 7. Richer Languages: Fixed-point operators and dynamics extensions 8. Richer Languages: First-order extensions

June 1st: Lecture 1 @ 14h00-16h30, F1.15 ILLC

June 2nd: Lecture 2 @ 12h30-14h30, F1.15 ILLC

June 7th: Lecture 3 @ 14h00-16h30, F1.15 ILLC

June 8th: Lecture 4 @ 11h00-13h00 and Lecture 5 @ 14h00-16h30, F1.15 ILLC

June 9th: Lecture 6 @ 12h30-14h30, F1.15 ILLC

June 13th: Lecture 7 @ 12h30-15h00, F1.15 ILLC

June 14th: Lecture 8 @ 10h00-13h00, F1.15 ILLC

June 15th: Presentations (solutions to problems etc.) @ 10h00-13h00, F1.15 ILLC

Prerequisites: There are no specific prerequisites, although some background on model logic will be helpful.

Assessment: Students can either write a paper or answers problems from the textbook. Students will be given an opportunity to present answers to the exercises.