In this paper we discuss the nature of independence of sources in the theory of evidence from an algebraic point of view. Independence in Dempster’s rule is equivalent to independence of frames IF as Boolean sub-algebras. IF , however, cannot be explained neither in terms of classical matroidal independence, nor (even if finite families of frames form geometric lattices) as a cryptomorphic form...

Recent years have seen increased interest in the question of whether it is possible to provide an evolutionary game theoretic explanation for certain kinds of social norms. I sketch a proof of a general representation theorem for a large class of evolutionary game theoretic models played on a social network, in hope that this will contribute to a greater understanding of the long-term evolution...

Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra structure, like in topos theory, but ‘characteristic’ functions, forming effect algebras. Such effect algebras are algebraic models of quantitative logic, in whi...

In this paper, we develop a theory of covers for funct ions defined over boolean str ings. Given a function , a cover is a decomposition , though not necessarily a partition, of the bits into subproblems that can be solved in parallel. In the paper , we formulat e th e notion of cover size , which equals the size of the largest subproblem in a decomposition for a parti cular function. Cover siz...

This paper includes two main ideas. The first one, rewriting in an algebra, was introduced in [5]. The second one, boolean rewriting, can be found in many papers but we were never able to find a clear comparison with the classic one. We prefer rewriting in an algebra to term rewriting. This is our way to give a unique theory of rewriting. If the algebra is free, then we get the term rewriting. ...

We consider the approximation problem of a pseudo-Boolean function by a symmetric pseudo-Boolean function in the sense of weighted least squares. We give explicit expressions for the approximation and provide interpretations and properties of its L-statistic representation. We also discuss applications of these expressions in cooperative game theory and engineering reliability.

If you want to cite this report, please use the following reference instead: B. De Schutter and B. De Moor, " On the sequence of consecutive powers of a matrix in a Boolean algebra, " SIAM Abstract. In this paper we consider the sequence of consecutive powers of a matrix in a Boolean algebra. We characterize the ultimate behavior of this sequence, we study the transient part of the sequence and...