In this paper we present a powerful uniform first-order framework for representing and reasoning with complex forms of default knowledge. This is achieved by extending first-order predicate logic with a new generalized quantifier, anchored in the quasi-probabilistic ranking measure paradigm [Weydert 94], which subsumes and refines the original, propositional notion of a default conditional [Del...

Ranking measures are coarse-grained, quasi-probabilistic plausibility valuations measuring the degree of surprise. Since Spohn’s work on the subclass of natural conditional functions, they have been used to model epistemic states and their dynamics. The simplest instance may be elementary ranking revision, which is a non-parametrized version of Spohn-style revision based on minimal Jeffreycondi...

Contents Introduction 3 Chapter 1. Mathematical preliminaries 13 1.1. Functions 13 1.2. Quasi-minima 15 1.3. Measures 18 Chapter 2. Compatible systems of Young measures: the stochastic process formulation and the discrete case 25 2.1. Compatible systems of Young measures 25 2.2. The probabilistic formulation 28 2.3. The discrete case 34 Chapter 3. Globally stable quasistatic evolution 39 3.

We consider the BDDC preconditioner for Reissner-Mindlin plate problems, discretized with the MITC element, introduced and analyzed in [11]. In that contribution the authors prove that the condition number of the ensuing linear system is independent of the plate thickness and scalable with respect to the mesh. We here prove, in addition, that the BDDC preconditioner of [11] is also quasi-optima...

We derive an asymptotic Newton algorithm for Quasi Maximum Likelihood estimation of the ICA mixture model, using the ordinary gradient and Hessian. The probabilistic mixture framework can accommodate non-stationary environments and arbitrary source densities. We prove asymptotic stability when the source models match the true sources. An application to EEG segmentation is given.

The purpose of the present notes is to examine following issues related Chernoff estimate: (1) For contractions on a Banach space we modify $\sqrt{n}$-estimate and apply it in proof product formula for $C_0$-semigroups \textit{strong} operator topology. (2) We use idea {probabilistic} approach, proving estimate strong topology, uplift \textit{operator-norm} \textit{quasi-sectorial} contraction ...

In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values Weber (1988) and quasi-probabilistic Bilbao et al. (2001). Applications to Multi-Touch Attribution interpretability Machine-Learning prediction models motivate these new developments (Lundberg Lee, 2017; Ribeiro al., 2016; Strumbelj Kononenko, 2013; Shrikumar Datta Bach 2015). We de...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

We consider quasi-variational inequalities (QVIs) with general non-local drivers and related systems of reflected backward stochastic differential equations (BSDEs) in a Brownian filtration. show existence uniqueness viscosity solutions to the QVIs by first considering standard (local) setting then applying contraction argument. In addition, argument yields BSDEs extends theory probabilistic re...