In the rough-set model, a set is represented by a pair of ordinary sets called the lower and upper approximations. In the interval-set model, a pair of sets is referred to as the lower and upper bounds which define a family of sets. A significant difference between these models lies in the definition and interpretation of their extended set-theoretic operators. The operators in the rough-set mo...

In the paper a survey on non conventional preference modeling is presented. Some philo-sophical discussion on the logic and foundations of human preferences is presented as the firstattempt to provide an axiomatization of the subject. The use of preference models in decisionaid however introduces such parameters to put serious questions to the possibility to build acomplete norm...

Partial functions are abundant in mathematics and program specifications. Unfortunately, their importance has been mostly ignored in automated theorem proving. In this paper, we develop a theorem proving strategy for Partial Classical Logic (PCL). Proof search takes place in Kleene Logic. We show that PCL theories can be translated into sets of formulas in Kleene logic. For proof search in Klee...

In this article techniques borrowed from Computer Algebra (Gröbner Bases) are applied to deal with Medical Appropriateness Criteria including uncertainty. The knowledge was provided in the format of a table. A previous translation of the table into the format of a “Rule Based System” (denoted RBS) based on a three-valued logic is required beforehand to apply these techniques. Once the RBS has b...

GROOLS (Genomic Rule Oriented Object Logic System) is an expert system to help biologists in the evaluation of genome functional annotation through biological processes like metabolic pathways. Such reasoning is conducted using a Business Rule Management System (BRMS) working on a generic representation of biological knowledge that captures complex data and relationships. We use the Object-Orie...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

This paper is gives a short introduction into HomotopyContinuation.jl, a polynomial equations solver for Julia [4]. It present excerpts from the comprehensive documentation available at https://juliahomotopycontinuation.github.io/latest/. The aim of this project is twofold: establishing a fast numerical polynomial solver in Julia and at the same time providing a highly customizable algorithmic ...

In this paper, we show that it is possible to accomplish belief revision in any logic which is translatable to classical logic. We start with the example of the propositional modal logic K and show that a belief operation in K de ned in terms of K0s translation to classical logic veri es the AGM postulates. We also consider the case of non-classical logics by taking Belnap's four-valued logic [...