We present a complete pretopology semantics for a system of Intuitionistic Linear Logic (commutative or not) where the storage operator is split into a contraction and a weakening component and then recovered again from them. The semantics for weakening and contraction has been explored by Bart Jacobs 13] in a categorical setting. However, a completeness theorem is not given in 13] and the appr...

This paper presents our participation to the SemEval Task-17, related to “Taxonomy Extraction Evaluation” (Bordea et al., 2015). We propose a new methodology for semisupervised and auto-supervised acquisition of lexical taxonomies from raw texts. Our approach is based on the theory of pretopology which offers a powerful formalism to model subsumption relations and transforms a list of terms int...

Pollution in metropolitan cities has become a serious problem, resulting in poor living conditions and serious health problems. Pollution being qualified as a complex system, we propose a multi-agent approach to model and simulate it, so that we could study, analyze and predict it better. As in the early stage of the project, we have some successful experiments and attempts to integrate the mat...

In nature, one observes that a K-theory of an object is defined in two steps. First a “structured” category is associated to the object. Second, a K-theory machine is applied to the latter category that produces an infinite loop space. We develop a general framework that deals with the first step of this process. The K-theory of an object is defined via a category of “locally trivial” objects w...

Let G be a non-finite profinite group and let G− Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G− Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. Also...

New economic and enterprise needs have increased the interest and utility of the methods of the grouping process based on the theory of uncertainty. A fuzzy grouping (clustering) process is a key phase of knowledge acquisition and reduction complexity regarding different groups of objects. Here, we considered some elements of the theory of affinities and uncertain pretopology that form a signif...

Let G be a non-finite profinite group and let G−Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G−Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. We poi...

Let G be a non-finite profinite group and let G− Setsdf be the canonical site of finite discrete G-sets. Then the category R G, defined by Devinatz and Hopkins, is the category obtained by considering G − Setsdf together with the profinite G-space G itself, with morphisms being continuous G-equivariant maps. We show that R G is a site when equipped with the pretopology of epimorphic covers. Als...

In this paper, we propose a new methodology for semisupervised acquisition of lexical taxonomies. Our approach is based on the theory of pretopology that offers a powerful formalism to model semantic relations and transforms a list of terms into a structured term space by combining different discriminant criteria. In order to learn a parameterized pretopological space, we define the Learning Pr...

We introduce the notion of infinitary preorder and use it to obtain a predicative presentation of sup-lattices by generators and relations. The method is uniform in that it extends in a modular way to obtain a presentation of quantales, as “sup-lattices on monoids”, by using the notion of pretopology. Our presentation is then applied to frames, the link with Johnstone’s presentation of frames i...