Closure and Causality

We present a model of causality which is defined by the intersection of two distinct closure systems, I and T . To present empirical evidence to demonstrate that this model has practical validity we then examine computer trace data to reveal causal dependencies between individual code modules. From over 498,000 events in an open source system, we tease our 66 apparent causal dependencies. Finally, we explore how to mathematically model the transformation of the causal topology resulting from unfolding events. 1 Closure Systems Let U denote some universe of elements. A closure system, C, is any collection of subsets X, Y, . . . Z U, including U itself, which is closed under intersection. Subsets in C are said to be closed. If U = {a, b, c, d, e} then the collection of closed sets C1 = {

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: John L. Pfaltz
• Keywords: Closure Operators, Closure Systems, DAGSTUHL 2006, DAGSTUHL 2007, Y Closure