We develop an alternative approach to well-ordering proofs beyond the Bachmann-Howard ordinal using transsnite sequences of ordinal notations and use it in order to carry out well-ordering proofs for-ordinal systems. We extend the approach of ordinal systems as an alternative way of presenting ordinal notation systems started in Set98b] and develop ordinal systems, which have in the limit exact...

We show that classification rules used in ordinal regression are equivalent to a certain class of linear multi-class classifiers. This observation not only allows to design new learning algorithms for ordinal regression using existing methods for multi-class classification but it also allows to derive new models for ordinal regression. For example, one can convert learning of ordinal classifier...

This paper presents a structured ordinal measure method for video-based face recognition that simultaneously learns ordinal filters and structured ordinal features. The problem is posed as a non-convex integer program problem that includes two parts. The first part learns stable ordinal filters to project video data into a large-margin ordinal space. The second seeks self-correcting and discret...

How can we grasp the temporal structure of events? A few studies have indicated that representations of temporal structure are acquired when there is an intention to learn, but not when learning is incidental. Response-to-stimulus intervals, uncorrelated temporal structures, unpredictable ordinal information, and lack of metrical organization have been pointed out as key obstacles to incidental...

dental caries is one of the most preventable yet prevalent chronic diseases worldwide. our objective was to evaluate the effect of family structure and behavioral and eyesight problems as they relate to caries severity in schoolchildren.this research was carried out on 845 primary schoolchildren aged 9 yr in kerman, iran, in 2012. ten variables, including health records, family structure inform...

Ordinal regression problem arises in situations where examples are rated in an ordinal scale. In practice, labeled ordinal data are difficult to obtain while unlabeled ordinal data are available in abundance. Designing a probabilistic semi-supervised classifier to perform ordinal regression is challenging. In this work, we propose a novel approach for semi-supervised ordinal regression using Ga...

We investigated the acquisition and integration of temporal and ordinal sequence information in an incidental learning model of motor skill acquisition (the serial reaction time task). Human participants were exposed to a stimulus-response sequence that had temporal structure, ordinal structure, or both. By changing the temporal or ordinal structure, or both, we were able to ask two questions: ...

Let λH be the term calculus of Howard’s system of constructive ordinals. I use this to name iteration gadgets (generalized ordinal notations). I isolate a family of higher order ordinal functions which give a partial semantics of λH. I indicate how λH provides an intrinsic measure of each ordinal below the Howard ordinal.1

The notion of ordinal computability is defined by generalising standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. The fundamental theorem on ordinal computability states that a set x of ordinals is ordinal computable from ordinal parameters if and only if x is an element of the constructible universe L. In this paper we present a new proof o...