Ordinal analysis is a research program wherein recursive ordinals are assigned to axiomatic theories. According conventional wisdom, ordinal measures the strength of Yet what attendant notion strength? In this paper we present abstract characterizations that address question. First, characterize as partition Σ11-definable and Π11-sound theories, namely, whereby two theories equivalent if they h...

Ordinal categorial variables are a common case in regression modeling. Although the case of ordinal response variables has been well investigated, less work has been done concerning ordinal predictors. This article deals with the selection of ordinally scaled independent variables in the classical linear model, where the ordinal structure is taken into account by use of a difference penalty on ...

We describe the systems we have used for participating in Subtasks D (binary quantification) and E (ordinal quantification) of SemEval-2016 Task 4 “Sentiment Analysis in Twitter”. The binary quantification system uses a “Probabilistic Classify and Count” (PCC) approach that leverages the calibrated probabilities obtained from the output of an SVM. The ordinal quantification approach uses an ord...

We study sets of reals computable by ordinal Turing machines with a tape of length the ordinals that are steered by a standard Turing program. The machines halt at some ordinal time or diverge. We construct tree representations for ordinal semidecidable sets of reals from ordinal computations. The aim is to generalize uniformization results to classes of sets which are semi-decidable by computa...

Ordinal logistic regression is a statistical analysis method that can be used to model the relationship between an ordinal response variable and one or more explanatory variables. An ordinal variable is a categorical variable for which there is a clear ordering of the category levels. The explanatory variables may be either continuous or categorical. Estimating ordinal logistic regression model...

When measuring health inequality using ordinal data, analysts typically must choose between indices specifically based upon ordinal data and more standard indices using ordinal data, which has been transformed into cardinal data. This paper compares inequality rankings across a number of different approaches and finds considerable sensitivity to the choice between ordinal- and cardinal-based in...