On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Using performance measurement models for benefit realization with enterprise systems: The Queensland Government approach (Case Study)

A range of influences, technical and organizational, has encouraged the wide spread adaption of Enterprise Systems (ES). Nevertheless, there is a growing consensus that Enterprise Systems have in the many cases failed to provide the expected benefits to organizations. This paper presents ongoing research, which analyzes the benefits realization approach of the Queensland Government. This approach applies a modified Balance Scorecard. First, history and background of Queensland Government’s Enterprise Systems initiative is introduced. Second, the most common reasons for ES under performance are related. Third, relevant performance measurement models and the Balanced Scorecard in particular are discussed. Finally, the Queensland Government initiative is evaluated in light of this overview of current work in the area. In the current and future work, the authors aim to use their active involvement in Queensland Government’s benefits realization initiative for an Action Research based project investigating the appropriateness of the Balanced Scorecard for the purposes of Enterprise Systems benefits realization.