In this paper we discuss the nature of independence of sources in the theory of evidence from an algebraic point of view, starting from an analogy with projective geometries. Independence in Dempster’s rule is equivalent to independence of frames as Boolean algebras. Collection of frames, in turn, can be given several algebraic interpretations in terms of semimodular lattices, matroids, and geo...

Quantum reference frames are expected to differ from classical because they have implement typical quantum features such as fluctuations and correlations. Here, we show that correlations of variables, in particular time, restricted by their very nature being used for reference. Mathematically, this property is implemented imposing constraints on the system make sure variables not physical degre...

Abstract We propose a class of algebraic polynomial frames, which are computationally easier to implement than polynomial bases. We also discuss the weighted Lstability of our frames for 1 ≤ p ≤ ∞. Our analysis is based on orthogonal polynomials with respect to the weight in question, but the frame bounds are independent of the system of orthogonal polynomials used. In spite of the fact that al...

Possibility semantics. Possibility semantics for modal logic is a generalization of standard Kripke semantics. In this semantics, a possibility frame has a refinement relation which is a partial order between states, in addition to the accessibility relation for modalities. From an algebraic perspective, full possibility frames are dually equivalent to complete Boolean algebras with complete op...

We introduce frames as basic objects for the construction of transition systems, process graphs or au-tomata. We provide an algebraic notation for frames, and display some theoretical results.

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.

This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the de nition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to de ne validity of formulas: the class of frames and the class of Šn-valued frames. The latter structures are frames in which we specify in each wor...