Sajad Nazari

Sajad Nazari
INSA Centre Val de Loire

PhD

About

13
Publications
1,258
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19
Citations

Publications

Publications (13)
Article
Full-text available
Let R be a commutative ring with identity and X be a Tychonoff space. An ideal I of R is Von Neumann regular (briefly, regular) if for every a ∈ I, there exists b ∈ R such that a = a²b. In the present paper, we obtain the general form of a regular ideal in C(X) which is OA, for some closed subset A of βX, for which Ac ∩ X ⊆ (P(X))◦, where P(X) is t...
Preprint
Let $R$ be a commutative ring, $Y\subseteq \mathrm{Spec}(R)$ and $ h_Y(S)=\{P\in Y:S\subseteq P \}$, for every $S\subseteq R$. An ideal $I$ is said to be an $\mathcal{H}_Y$-ideal whenever it follows from $h_Y(a)\subseteq h_Y(b)$ and $a\in I$ that $b\in I$. A strong $\mathcal{H}_Y$-ideal is defined in the same way by replacing an arbitrary finite se...
Preprint
Full-text available
The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original approximation spaces can be seen as special instances of enriched formal contexts, i.e. relational structures based...
Preprint
Full-text available
A recent line of research has developed around logics of belief based on information confirmed by a reliable source. In this paper, we provide a finer analysis and extension of this framework, where the confirmation comes from multiple possibly conflicting sources and is of a probabilistic nature. We combine Belnap-Dunn logic and non-standard proba...
Article
Full-text available
We characterize rings in which every left ideal generated by an idempotent different from 0 and 1 is either a maximal left ideal or a minimal left ideal. In the commutative case, we give a characterization in terms of topological properties of the maximal spectrum with the Zariski topology. We also consider a strictly weaker variant of this propert...
Chapter
[3] and [7] generalize the notion of probability measures and belief functions to Belnap-Dunn (\(\textsf{BD}\)) logic, respectively. This work aims at providing an alternative way to treat contradictory information by relying on a logic that was introduced to reason about incomplete and contradictory information rather than on classical logic. In t...
Preprint
Full-text available
Belief and plausibility are weaker measures of uncertainty than that of probability. They are motivated by the situations when full probabilistic information is not available. However, information can also be contradictory. Therefore, the framework of classical logic is not necessarily the most adequate. Belnap-Dunn logic was introduced to reason a...
Preprint
Full-text available
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and belief functions in two ways. First, using a calculus of linear inequalities, akin to the one presented in~\c...
Chapter
A recent line of research has developed around logics of belief based on evidence [4, 6]. The approach of [6] understands belief as based on information confirmed by a reliable source. We propose a finer analysis of how belief can be based on information, where the confirmation comes from multiple possibly conflicting sources and is of a probabilis...
Article
The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak’s original approximation spaces can be seen as special instances of enriched formal contexts, i.e. relational structures based...

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Projects

Project (1)
Project
considering the distributive semiprimitive PM-lattices, their characterizations according the spectra of the lattce