By and large, three classic framework models have been used in the process of retrieving information: Boolean, Vector Space and Probabilistic. Boolean model is a light weight model which matches the query with precise semantics. Because of its boolean nature, results may be tides, missing partial matching, while on the contrary, vector space model, considering term-frequency, inverse document f...

Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...

We present a method for determining the probability that a given point lies in the vacant region of a Boolean model subject to the condition that this probability takes imposed values on certain points. This method is based on a characterisation of the intensity of the Boolean model as a Young measure, such that after discretisation a large deviations principle holds; this induces a concentrati...

Cancellations are known to be helpful in e cient algebraic computation of polynomials over elds. We de ne a notion of cancellation in Boolean circuits and de ne Boolean circuits that do not use cancellation to be non-cancellative. Non-cancellative Boolean circuits are a natural generalization of monotone Boolean circuits. We show that in the absence of cancellation, Boolean circuits require sup...

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy “tops only.” That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third, . . . , or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean a...

Boolean Networks are emerging as a simple yet powerful formalism to model and study Gene Regulatory Networks. Nevertheless, the most widely used Boolean Network-based models do not include any post-transcriptional regulation mechanism. In this paper we discuss how the post-transcriptional regulation mechanism mediated by miRNAs can be included in a Boolean Network based model. This contribution...

We introduce Non-deterministic Boolean proof nets to study the correspondence with Boolean circuits, a parallel model of computation. We extend the cut elimination of Non-deterministic Multiplicative Linear logic to a parallel procedure in proof nets. With the restriction of proof nets to Boolean types, we prove that the cut-elimination procedure corresponds to Non-deterministic Boolean circuit...

A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the r...

We consider a weighted stationary spherical Boolean model in R. Assuming that the radii of the balls in the Boolean model have regularly varying tails, we establish the asymptotic behaviour of the tail of the contact distribution of the thinned germ-grain model under 4 different thinning procedures of the original model.

This paper presents a new Lambda-Boolean reduction machine for Lambda-Boolean and Lambda-Beta Boolean reductions in the context of Lambda Calculus and introduces the role of Church–Rosser properties and functional computation model in symbolic and algebraic computation with induction. The algorithm which improved for Lambda-Beta Boolean reduction is simulated by the efficient logical programmin...