Neighborhood Semantics for Modal Logic

ESSLLI 2014

Course Information

• Lecturer: Eric Pacuit (website)
• Venue: Tübingen, Germany
• Dates: August 11 - 16, 2014
• Meeting Times: 9:00am - 10:30am
• Course Overview

Day 1    Introduction and Motivation I

• Slides

• 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

• Slides

• 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

• Slides

• Topics : Relationship with plausibility structures; Completeness and incompleteness of non-normal modal logics

  Reading material : Chapter 2 (Core Theory)

Day 4    Core Theory II

• Slides

• 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

• Slides

• 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