Neighborhood Semantics for Modal Logic
Instructor: Eric Pacuit (website)
ESSLLI 2014 • Tübingen, Germany
August 11 - 16, 2014
9:00am - 10:30am
Day 1: Introduction and Motivation I
Topics : Introduce both relational and neighborhood semantics for modal
logic; Discuss key motivating for studying non-normal modal logics: Logics of
ability, Logics for group decision making, Logic of classical deductive
closure, Deontic logic paradoxes, the problem of logical omniscience and
knowledge closure; Normal and non-normal modal logics
Reading material : Chapter 1 (Introduction and
Motivation)
Day 2: Introduction and Motivation II
Topics : Neighborhood frames/models; Examples of logics using neighborhood
structures: A logic of knowledge, evidence and belief, Coalitional Logic,
Subset Space Logic (Topologic); Neighborhood semantics in the broader logical
landscape: relationship with relational structures, topological models, n-ary
relational models
Reading material : Chapter 1 (Introduction and
Motivation)
and Chapter 2 (Core Theory)
Day 3: Core Theory I
Topics : Relationship with plausibility structures; Completeness and
incompleteness of non-normal modal logics
Reading material : Chapter 2 (Core
Theory)
Day 4: Core Theory II
Topics : Decidability, Complexity, Definability, Model Theory
(bisimulations, relationship with first-order logic)
Reading Material
- H. Hvid Hansen, C. Kupke and E. Pacuit, Neighbourhood Structures: Bisimilarity and Basic Model Theory
- H. Hvid Hansen, Monotonic modal logics
Day 5: Core Theory II
Topics : First-order modal logic on neighborhood structures, Game Logic,
Dynamics on neighborhood structures
Reading Material
- H. Arlo-Costa and E. Pacuit, First-Order Classical Modal Logic,Studia Logica, 84(2), pgs. 171 - 210, 2006
- R. Parikh, Game Logic and its Applications, 1985
- J. van Benthem and E. Pacuit, Dynamic Logics of Evidence Based Beliefs, Studia Logica, 99, pgs. 61 - 92, 2011