
A Course on Neighborhood Structures for Modal Logic
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 selfcontained, 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 nonnormal 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.



Literature 


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: Nonnormal Modal Logics, Completeness 

Topics: completeness of nonnormal 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 nonnormal modal logics with normal modal logics, neighborhood semantics for firstorder modal logic
Lecture Slides


Day 4: Advanced Topics II 

Possible topics: some model theory  model constructions, comparison with firstorder 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



