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

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• 作者：Maurí ; cio D.L. Reis^a ; ^b ; ^{m_reis@uma.pt" class="auth_mail" title="E-mail the corresponding author} ; Eduardo Fermé ; ^a ; ^b ; ^{ferme@uma.pt" class="auth_mail" title="E-mail the corresponding author} ; Pavlos Peppas^c ; ^d ; ^{pavlos.peppas@uts.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Belief change ; Theory contraction ; Multiple contraction ; System of spheres ; (Transitively relational) partial meet
• 刊名：Artificial Intelligence
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：233
• 期：Complete
• 页码：122-141
• 全文大小：561 K

文摘

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 multiple contractions introduced in [17] and [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 contractions 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.