Commonsense knowledge representation and reasoning with fuzzy neural networks

This paper highlights the theory of common-sense knowledge in terms of representation and reasoning. A connectionist model is proposed for common-sense knowledge representation and reasoning. A generic fuzzy neuron is employed as a basic element for the connectionist model. The representation and reasoning ability of the model is described through examples

On the Equivalence of Forward Mode Automatic Differentiation and Symbolic Differentiation

We show that forward mode automatic differentiation and symbolic differentiation are equivalent in the sense that they both perform the same operations when computing derivatives. This is in stark contrast to the common claim that they are substantially different. The difference is often illustrated by claiming that symbolic differentiation suffers from "expression swell" whereas automatic differentiation does not. Here, we show that this statement is not true. "Expression swell" refers to the phenomenon of a much larger representation of the derivative as opposed to the representation of the original function

Knowledge of individual histories and optimal payment arrangements.

This article reviews recent work that generalizes a random matching model of money to permit there to be a mix of transactions: some accomplished through the use of tangible media of exchange and the rest through some form of credit. The generalizations are accomplished by specifying assumptions about common knowledge of individual histories that are intermediate between no common knowledge and complete common knowledge. One of the specifications permits a simple representation of the sense in which more common knowledge is beneficial. The other permits a comparison between using outside money and using inside money as a medium of exchange.Money ; Credit

Compact κ\kappa-deformation and spectral triples

We construct discrete versions of $\kappa$-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical system of the underlying discrete groups (which include some Baumslag--Solitar groups) is heavily used in order to construct \emph{finitely summable} spectral triples. This allows to bypass an obstruction to finite-summability appearing when using the common regular representation. The dimension of these spectral triples is unrelated to the number of coordinates defining the $\kappa$-deformed Minkowski spaces.Comment: 30 page

La physique naïve: un essai d'ontologie

The project of a naive physics has been the subject of attention in recent years above all in the artificial intelligence field, in connection with work on common-sense reasoning, perceptual representation and robotics. The idea of a theory of the common-sense world is however much older than this, having its roots not least in the work of phenomenologists and Gestalt psychologists such as Kohler, Husserl, Schapp and Gibson. This paper seeks to show how contemporary naive physicists can profit from a knowledge of these historical roots of their discipline, which are shown to imply above all a critique of the set-theory-based models of reality typically presupposed by contemporary work in common-sense ontology

Criteria for Proportional Representation

Methods to allocate seats in proportional representation systems are investigated in terms of several underlying common-sense properties. In particular, the idea of stability is introduced, and the method of Jefferson (or d'Hondt) is characterized