Neighborhood Semantics for Modal Logic
Language & Logic
Week One - 9.00-10.30 - Level: A
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 the family of classical modal logics, including many interesting non-normal modalities from Concurrent Propositional Dynamic Logic to Coalitional Logic to weak systems of beliefs used in various branches of game theory. 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. In this course, I will introduced the basic techniques and results of neighborhood semantics for modal logic and explain the exact relationship between the standard relational semantics and neighborhood semantics 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.