Paradeduction in Axiomatic Formal Systems

The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any logic, introduced as an axiomatic formal system, into a paraconsistent one

Is nature OO?

What exists "out there"? What does "doing physics" mean? What are the axiomatic ideas for microphysics? What is a particle? What is an apparatus made of? We show that Quantum Mechanics textbooks cannot truly answer this kind of question whereas they should. By adopting a pure "hitological" point of view for microphysics, we introduce the Hit in Apparatuses Theory (HAT) and the Vacuum of Apparatuses (VA) that restore, through Object Orientation (OO), an intuitive ontology to deal with this kind of physics. Through a review of what it means to "observe" and what relativism means in Special and General Relativities (SR and GR), we address the problem of finding common maths for GR and QM. Finally, with our new HAT, we address the measurement problem in QM and propose two possible approaches.Comment: 26 page

Valuable or Stagnating? An Essay on Axiomatic Theories in IS Research

An axiomatic theory is theory whose premise is so self-evident that it can be accepted as true without controversy or much empirical confirmation. In this paper, I entertain the contention that theorizing in information systems (IS) research is mostly axiomatic. If so, among the many ramifications are questions regarding the value relevance of such research. After all, if the field engages in creating theories that are in plain-view, self-evident, and can be deduced using common sense, what is the knowledge contribution of such endeavors? Is there value in producing such theories or is the effort invested in testing these kinds of theories a waste of precious resources? Has our preoccupation with axiomatic theories led to theoretical stagnation in the field? In this essay, I investigate the nature of axiomatic theories and make the case that much significant research in IS is not axiomatic

What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery

Data Discovery and Anomaly Detection Using Atypicality: Theory

A central question in the era of 'big data' is what to do with the enormous amount of information. One possibility is to characterize it through statistics, e.g., averages, or classify it using machine learning, in order to understand the general structure of the overall data. The perspective in this paper is the opposite, namely that most of the value in the information in some applications is in the parts that deviate from the average, that are unusual, atypical. We define what we mean by 'atypical' in an axiomatic way as data that can be encoded with fewer bits in itself rather than using the code for the typical data. We show that this definition has good theoretical properties. We then develop an implementation based on universal source coding, and apply this to a number of real world data sets.Comment: 40 page

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Influence in Classification via Cooperative Game Theory

A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely characterize an influence measure: a function that, given a set of classified points, outputs a value for each feature corresponding to its influence in determining the classification outcome. We show that our influence measure takes on an intuitive form when the unknown classifier is linear. Finally, we employ our influence measure in order to analyze the effects of user profiling on Google's online display advertising.Comment: accepted to IJCAI 201