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...