Construction of system of spheres-based transitively relational partial meet multiple contractions: An impossibility result
- Publication Type:
- Journal Article
- Citation:
- Artificial Intelligence, 2016, 233 pp. 122 - 141
- Issue Date:
- 2016-04-01
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© 2016 Elsevier B.V. All rights reserved. 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 [17,5] 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.
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