Applying relational algebra and RelView to measures in a social network

We present an application of relation algebra to measure agents' 'strength' in a social network with influence between agents. In particular, we deal with power, success, and influence of an agent as measured by the generalized Hoede-Bakker index and its modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.RelView; relation algebra; social network; Hoede-Bakker index; influence index

Applying Relation Algebra and RelView to Measures in aSocial Network

We present an application of relation algebra to measure players' ‘strength' in a social network with influence between players. In particular, we deal with power, success, and influence of a player as measured by the Hoede-Bakker index, its generalization and modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDDbased tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.RelView ; relation algebra ; social network ; the Hoede-Bakker index ; influence index ;follower ; kernel

Social networks: Prestige, centrality, and influence (Invited paper)

We deliver a short overview of di erent centrality measures and influence concepts in social networks, and present the relation-algebraic approach to the concepts of power and influence. First, we briefly discuss four kinds of measures of centrality: the ones based on degree, closeness, betweenness, and the eigenvector-related measures. We consider centrality of a node and of a network. Moreover, we give a classi cation of the centrality measures based on a topology of network flows. Furthermore, we present a certain model of influence in a social network and discuss some applications of relation algebra and RelView to this model.social network ; centrality ; prestige ; influence ; relation algebra ; RelView

Computing Tournament Solutions using Relation Algebra and REL VIEW

We describe a simple computing technique for the tournament choice problem. It rests upon a relational modeling and uses the BDD-based computer system RelView for the evaluation of the relation-algebraic expressions that specify the solutions and for the visualization of the computed results. The Copeland set can immediately be identified using RelView's labeling feature. Relation-algebraic specifications of the Condorcet non-losers, the Schwartz set, the top cycle, the uncovered set, the minimal covering set, the Banks set, and the tournament equilibrium set are delivered. We present an example of a tournament on a small set of alternatives, for which the above choice sets are computed and visualized via RelView. The technique described in this paper is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other problems of social choice and game theory.Tournament, relational algebra, RelView, Copeland set, Condorcet non-losers, Schwartz set, top cycle, uncovered set, minimal covering set, Banks set, tournament equilibrium set.

Relation algebra : a tarskian axiomatization

Orientador: Itala Maria Loffredo D'OttavianoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências HumanasResumo: Em 1975, Alfred Tarski, um dos maiores lógicos contemporâneos, visitou o Instituto de Matemática, Estatística e Ciência da Computação (IMECC) da Unicamp. Nessa oportunidade, foi organizado um evento, o Simpósio de Lógica Matemática, para recebê-lo. Tarski apresentou então sua axiomatização para o cálculo de relações, conhecida como álgebra de relações (RA). A RA, como teoria formal desenvolvida por Tarski, foi apresentada em duas conferências, que foram pioneiramente gravadas em fita de vídeo e atualmente fazem parte do acervo dos Arquivos Históricos do Centro de Lógica, Epistemologia e História da Ciência (CLE) da Unicamp. Neste trabalho, apresentamos uma transcrição das conferências de Tarski e examinamos o seu conteúdo, inserindo-o no contexto histórico do desenvolvimento da teoria do cálculo de relações, cujo início remonta à alguns trabalhos de De Morgan, Peirce e Schröder. Tendo em vista que a origem dessa teoria já foi devidamente abordada, concentrar-nos-emos mais no conteúdo das conferências de Tarski proferidas no Brasil, sobre RA, dando especial atenção aos problemas deixados em aberto nessa ocasião, e no recente desenvolvimento de sua teoria.Abstract: In 1975, Alfred Tarski visited the Instituto de Matemática, Estatástica e Ciência da Computação (IMECC) at Unicamp, Brazil. In that ocasion, an event was organized to welcome him, the Simpósio de Lógica Matemática. Tarski's talking was about his axiomatization on the calculus of relations, which in that time was already known as Relation Algebra (RA). In Brazil, the formal theory of RA developed by Tarski was introduced to his audience in two lectures, which were taped and nowadays belongs to the historical files of Arquivos Hist'oricos do Centro de Lógica, Epistemologia e História da Ciência (CLE) at Unicamp. Our work aims to bring Tarski's conferences for public access through our transcription of them, and besides that, it is also our aim to analize Tarski's lectures and put it into the historical context of the development of RA, which origin goes back to some works of De Morgan, Peirce and Schröder. Our focus is on the content of the conferences, specially on the open problems left by Tarski and on the recent development of his theory.MestradoMestre em Filosofi