Local Dependence

Toby Meadows (Bristol) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Local Dependence". Abstract: The purpose of this paper is to lay out some groundwork for a general understanding of relationships between: notions of dependence and groundedness; and notions of complexity and cardinality. We commence by sketching a pleasing framework linking dependence with the theory of inductive definitions. We pose a kind of problem for this framework and attempt to explain why this is interesting using a case study from the semantic theory of truth literature. We then attempt to formulate a definition of local dependence which addresses this issue. Finally, we consider limitations of this definition and consider possibilities for its further generalisation.