Construction of system of spheres-based transitively relational partial meet multiple contractions: an impossibility result

• Autor(a) principal: Reis, Maurício D. L.
• Data de Publicação: 2016
• Outros Autores: Fermé, Eduardo, Peppas, Pavlos
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.13/3444
• topic: Belief change; Theory contraction; Multiple contraction; System of spheres; Transitively relational; .; Faculdade de Ciências Exatas e da Engenharia

In this paper we show that, contrary to what is the case in what concerns contractions by a single sentence, there is not a system of spheres-based construction of multiple contractions which generates each and every transitively relational partial meet multiple contraction. Before proving the general result, we consider the class of system of spheres-based mul tiple contractions introduced in [17,5] and show that this class neither subsumes nor is subsumed by the class of transitively relational partial meet multiple contractions. Furthermore, we propose two system of spheres-based constructions of multiple con tractions which generate (only) transitively relational partial meet multiple contractions. Therefore we can conclude that, although it is impossible to obtain a system of spheres based definition of all the transitively relational partial meet multiple contractions, there are classes of system of spheres-based multiple contractions which are subsumed by the class of transitively relational partial meet multiple contractions.