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...

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...

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...

We introduce the principle of robust ordinal regression to group decision. We consider the main multiple criteria decision methods to which robust ordinal regression has been applied, i.e., UTA and GRIP methods, dealing with choice and ranking problems, UTADIS , dealing with sorting (ordinal classification) problems, and ELECTRE , being an outranking method applying robust ordinal regression to...