It is assumed that a Kripke-Joyal semantics A = 〈C,Cov,F, 〉 has been defined for a first-order language L. To transform C into a Heyting algebra C on which the forcing relation is preserved, a standard construction is used to obtain a complete Heyting algebra made up of cribles of C. A pretopology Cov is defined on C using the pretopology on C. A sheaf F is made up of sections of F that obey fu...

Studies in social network analysis consider the behavior of a group to be equivalent to the “sum” of individual behaviors. However, a group has to be considered as a complex system where emerging phenomena can appear. In this paper, a formalism is proposed to resolve this problematic by modeling groups in social networks using pretopology as a generalization of the graph theory. We also give an...

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

The aim of this article is to present a methodological approach for problems encountered in structural analysis of web communities. This approach is based upon the pretopological concepts of pseudoclosure and the searching of equivalent nodes. The advantage of this approach is that it provides a framework needed to pass through the actual limits of graph theory modeling. The problem of modeling...

The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped at least with a notion of distance, for example, a Euclidean vector space. Recent computational work on the biophysical genotype-phenotype model defined by the folding of RNA sequences into secondary structures s...

Pretopologies were introduced in [S] and there shown to give a complete semantics for a propositional sequent calculus BL here called basic linear logic, as well as for its extensions by structural rules, ex falso quodlibet or double negation. Immediately after the Logic Colloquium ’88, conversation with Per Martin-Löf helped me to see how the pretopology semantics should be extended to predica...

Granular computing (GrC) is a methodology or – as ambitious at it sounds – a paradigm in computer science the aim of which is to define and solve computational problems in terms of information granules. These granules are conceived as clumps of objects drawn together due to some criteria such as, e.g., similarity, indiscernibility or functionality. The present paper is concerned with the rough ...