Approximately speaking, an urn model for first-order logic is a model where the domain of quantification changes depending on the values of variables which have been bound by quantifiers previously. In this paper we introduce a modelchanging semantics for urn-models, and then give a sequent calculus for urn logic by introducing formulas which can be read as saying that “after the individuals a1...

The talk1 describes an analytic approach to urn models of the Pólya type where an urn may contain balls of either of two colours. At each step, a ball is randomly drawn and replaced by balls of the two colours; a fixed 2× 2-matrix with constant row sum determines the replacement policy. The treatment starts from a partial differential equation associated with the model and bases itself on confo...

Technologies based on aspects and applied at the early stages of software development allow requirements engineers to better encapsulate crosscutting concerns in requirements models. The Aspect-oriented User Requirements Notation (AoURN) extends the User Requirements Notation (URN) with aspects and thus unifies goal-oriented, scenariobased, and aspect-oriented concepts in one framework. Minimal...

The Pólya urn has been extensively studied and is widely applied in many disciplines. An important application is to use urn models to develop randomized treatment allocation schemes in clinical studies. As an extension of the Pólya urn, the randomly reinforced urn was recently proposed to optimize clinical trials in the sense that patients are assigned to the best treatment with probability co...

The User Requirements Notation (URN) is a standard modeling language that includes two complementary views, one for goals with the Goaloriented Requirement Language (GRL) and one for scenarios/processes with Use Case Maps (UCM). The URN standard, however, does not provide means of checking consistency between the GRL and UCM views, leading to models that are potentially erroneous. This paper pr...

We study an urn model introduced in the paper of Chen and Wei [2], where at each discrete time step m balls are drawn at random from the urn containing colors white and black. Balls are added to the urn according to the inspected colors, generalizing the well known Pólya-Eggenberger urn model, case m = 1. We provide exact expressions for the expectation and the variance of the number of white b...

Yao's formula is one of the basic tools in any situation where one wants to estimate the number of blocks to be read in answer to some query. We show that such situations can be modelized by probabilistic urn models. This allows us to fully characterize the distribution probability of the number of selected blocks under uniformity assumptions, and to consider extensions to non-uniform block pro...

This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2, . . . , n− 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition a...

This work is devoted to the analysis of the area under certain lattice paths. The lattice paths of interest are associated to a class of 2 × 2 triangular Pólya-Eggenberger urn models with ball replacement matrix M = (−a 0 c −d ) , with a, d ∈ N and c = p · a, p ∈ N0. We study the random variable counting the area under sample paths associated to these urn models, where we obtain a precise recur...