A Course on Neighborhood Structures for Modal Logic

12 - 17 August, 2007
European Summer School for Logic, Language and Infromation

Dublin, Ireland

Course Information
| Literature | Course Schedule (Day 1, Day 2, Day 3, Day 4, Day 5)


Course Information


Intstructor: Eric Pacuit (ILLC, University of Amsterdam)

Prerequisites: Although the course will be self-contained, it is recommended to have basic knolwedge of modal logic. For example, it will be useful to be familiar with:

1. The first four chapters (skipping the advanced track sections) of Modal Logic by P. Blackburn, M. de Rijke and Y. Venema (Cambridge University Press, 2001).

- and/or -

2. Modal Logic: an Introduction by Brian Chellas (Cambridge University Press, 1980).

Content: Dana Scott and Richard Montague (influenced by a paper written by McKinsey and Tarski in 1944) proposed independently in 1970 a new semantic framework for the study of modalities, which today is known as neighborhood semantics. The semantic framework permits the development of elegant models for the family of classical modal logics, including many interesting non-normal modalities from Concurrent Propositional Dynamic Logic, to Coalitional Logic to various monadic operators of high probability used in various branches of game theory. I will introduce neighborhood semantics for modal logic and discuss some applications. The main goal of the corse is to understand the basic techniques and results of neighborhood semantics for modal logics and to understand the exact relationship between the standard relational semantics and neighborhoood semantics for modal logics.




Neighborhood Semantics for Modal Logic: An Introduction (version July 3, 2007): Course notes that include an introduction to neighborhood semantics and extended bibliography.

Two other sources will be useful for the course:

1. Helle Hvid Hansen, Monotonic modal logics, Master's Thesis, Institute for Logic, Language and Information (2003). [pdf]

2. Brian Chellas, Modal Logic: an Introduction (Cambridge University Press, 1980) chapters 7 - 9 cover basic results about classical modal logic.


Course Schedule


Note that this schedule is only a tenative outline and may change as the

Day 1: Introduction, Motivation and Basic Concepts
  Topics: introduce some basic concepts of neighborhood semantics for modal logic and discuss some motivating examples. (Sections 1 & 2 of the course notes.)

Lecture Slides
Day 2: Non-normal Modal Logics, Completeness

Topics: completeness of non-normal modal logics with respect to neighborhood frames. (Section 3 of the course notes.), a few comments on incompletness.

Lecture Slides

Day 3: Advanced Topics I
  Topics: topological semantics for modal logic, subset spaces, simulating non-normal modal logics with normal modal logics, neighborhood semantics for first-order modal logic

Lecture Slides
Day 4: Advanced Topics II
  Possible topics: some model theory --- model constructions, comparison with first-order logic, bisimulations

Lecture Slides
Day 5: Extensions and Applications
  Possible topics: The proof of a Van Benthem Characterization Thoerem for Classical Modal Logic; sketching further topics: more on simulations, algebra, coalgebra, common knowledge/beliefs; neighborhood semantics in action: concurrent PDL, game logic

Lecture Slides