If you want to know whether a property is true or not in a specific algebraic structure, you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testi...

We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density, becomes implicit, and can have non-unique solutions. We investigate the well-posedness of the model and show rigorously how it can be obtained as ...

Information extraction (IE) is the problem of constructing a knowledge base from a corpus of text documents. In this paper, we argue that firstorder probabilistic models (FOPMs) are a promising framework for IE, for two main reasons. First, FOPMs allow us to reason explicitly about entites that are mentioned in multiple documents, and compute the probability that two strings refer to the same e...

First-order Markov models have been successfully applied to many problems, for example in modeling sequential data using Markov chains, and modeling control problems using the Markov decision processes (MDP) formalism. If a first-order Markov model’s parameters are estimated from data, the standard maximum likelihood estimator considers only the first-order (single-step) transitions. But for ma...

We present a framework in which partial order plans are used for project management tasks where the dependency between each sub task and employee can be observed. For this purpose, extending the resource conscious linear logic planning, we establish an explicit correspondence between multiplicative exponential linear logic proofs and partial order plans. We express planning problems as formulae...

A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduce...

There has been a long standing division in Artificial Intelligence between logical and probabilistic reasoning approaches. While probabilistic models can deal well with inherent uncertainty in many real-world domains, they operate on a mostly propositional level. Logic systems, on the other hand, can deal with much richer representations, especially first-order ones, but treat uncertainty only ...

We study certain nonlinear continuous models of opinion formation derived from a kinetic description involving exchange of opinion between individual agents. These models imply that the only possible final opinions are the extremal ones, and are similar to models of pure drift in magnetization. Both analytical and numerical methods allow to recover the final distribution of opinion between the ...

Abstract In this letter, we exploit the Damour-Deruelle solution to derive analytical expression of coordinate time in terms polar angle. This formula has advantageous applications both pulsar timing and gravitational-wave theory.