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

Day 5: Core Theory II

Topics : First-order modal logic on neighborhood structures, Game Logic,
Dynamics on neighborhood structures

Reading Material