Andrei Rusu

Universitatea Ovidius Constanţa | UOC · Faculty of Mathematics and Informatics

The technologies used for building, maintaining and thriving digital repositories by fields of specialization using open source and free-to-use technologies in order to promote the digitization of the internationally recognized scientific heritage in mathematics and computer science are analyzed and presented.

At present, there are important changes in scientific research, changes that concern both the organization, realization and evaluation of research, as well as the use and dissemination of scientific results. These changes that are characteristic to the Open Science phenomenon are determined by the development of new technologies, by increasing the...

It is well known the connection of diagonalizable algebras with propositional provability logics. The notion of expressibility of functions and related algorithmic problems is very well studied in the case of boolean functions. We propose and analyse algorithms for detecting functional expressibility of functions of a 4-valued diagonalizable algebr...

The Open Science concept represents a new approach to the way in which scientific research based on cooperation and new ways of knowledge dissemination is carried out and organized, using new digital technologies, new tools for collaboration, and R&D infrastructure to ensure open access to research data. This study uses data collected in May - July...

Open Science requires a new systemic approach, particularly in terms of national and international strategies and policies. Open Science policies need to be promoted and implemented in the Republic of Moldova. The current study makes an overview of the "Open Science" concept, as well as international experiences, necessary to better understand the...

Currently the science and innovation area of the Republic of Moldova is undergoing an extensive process of transformation aiming to increase the effectiveness, to facilitate the inclusion of national science into the ERA. Taking into account that the European integration is a major priority for the Republic of Moldova, the public research and innov...

In the present paper we consider the expressibility of formulas in the provability logic GL and related to it questions of the model completeness of system of formulas. We prove the absence of a finite approximation relative to model completeness in GL.

In the present paper we consider a non-tabular extension

In the present paper we consider the simplest non-classical extension $GL4$ of the well-known propositional provability logic $GL$ together with the notion of expressibility of formulas in a logic proposed by A. V. Kuznetsov. Conditions for expressibility of constants in the 4-valued extension $L\mathfrak{B}_2$ of $GL$ are found out, which were fir...

In the present paper we show that there are infinitely many classes of term functions in the free-void generated diagonalizable algebra, which are precomplete with respect to parametrical expressibility of functions.

We present a rather simple example of infinitely many maximal primitive positive clones in a diagonalizable algebra, which serve as an algebraic model for the provability propositional logic GL.

Summary: We consider the propositional provability intuitionistic logic $I^Delta$, introduced by A. V. Kuznetsov. We prove that there are infinitely many classes of formulas in the calculus of $I^Delta$, which are pre-complete with respect to functional expressibility in $I^Delta$. This result is stronger than an ealier one obtained by the author.

The paper is devoted to the problem of definability, in particular to the question of completeness. The main result consists in constructing an example of an $m$-pre-complete (with respect to functional expressibility) class of formulas in the propositional provability logic.

Summary: The idea of embedding intuitionistic logic into modal logic and the following interpretation of the modality as a provable deducibility in Peano arithmetic and also the difficulties arising here are well known. R. M. Solovay and A. V. Kuznetsov introduced the Gödel-Löb provability logic in which formulas consist of propositional variables...

Summary: Necessary and sufficient conditions for a system of formulas to be complete with respect to expressibility in a 4-valued extension of the provability logic of propositions are shown in the article.

We present necessary and sufficient conditions for a system of functions of a 4-valued diagonalizable algebra to be complete in this algebra.

Summary: The provability logic $G$ permits to immerse intuitionistic logic into Peano Arithmetic. Its formulas are built up with the connectives $&$, $vee$, $supset$, $neg$, $Delta$. A system $Sigma$ of formulas is called complete (with respect to expressibility) in the logic $L$ if all formulas are expressible via $Sigma$ in $L$. A system of formu...