KR Conference 2012 Short Paper
Revising partial pre-orders with partial pre-orders: A unit-based revision framework
- Jianbing Ma
- Salem Benferhat
- Weiru Liu
(Benferhat, Lagrue, and Papini 2005)). In (Benferhat et al. 2000), the epistemic state, representing initial information, and the input, representing new information, are both total pre-orders. In (Benferhat, Lagrue, and Papini 2005), the initial epistemic state is indeed a partial pre-order, however, the input information is a propositional formula. In (Bochman 2001), different strategies have been proposed to revise an epistemic state represented by a partial pre-order on the possible worlds. However, in this book there are no revision methods for revising a partial pre-order by a partial pre-order. Our revision operations are also totally different from Lang’s works on preference (e. g. (Lang and van der Torre 2008)), and Weydert, Freund and Kern-Isberner’s revision with conditionals (e. g., (Weydert 1994; Freund 1998; Kern-Isberner 2002)). So far in the literature, there is hardly any work that studies the revision of an epistemic state (especially a partial pre-order) being revised by a partial preorder (a new input). The only work we have seen addressing this issue is a recent paper (Tamargo et al. 2011), in which revision of partial orders is studied in a standard expansion and contraction way. But it does not provide concrete revision results because of the use of certain kinds of selection functions. In this paper, we investigate revision strategies for this setting: a partial pre-order revised by another partial preorder. With this perspective, each individual ordering relation (a pair of elements with an ordering connective), which we name unit, contained in the input is itself an important piece of evidence that should be preserved (Ma, Liu, and Hunter 2011). To propose a revision framework for partial pre-orders, we investigate how a revision operator should be designed. Generally speaking, both a priori ordering set, S, and a new input SI can be seen as sets containing individual ordering relations, e. g., the units. So, revision can be carried out by (i) deriving maximal supersets of SI that contain suitable units in S which do not lead to possible contradiction; (ii) by inserting units from SI to S while removing any units that are inconsistent with this insertion; or (iii) by enlarging SI through inserting one unit from S at a time, while maintaining consistency, etc. Based on these intuitions, we propose a family of unit-based revision operators, dubbed extension revision, match revision, inner revision, and outer revision. We prove the equivalence between these operators Belief revision studies strategies about how agents revise their belief states when receiving new evidence. Both in classical belief revision and in epistemic revision, a new input is either in the form of a (weighted) propositional formula or a total pre-order (where the total pre-order is considered as a whole). However, in some real-world applications, a new input can be a partial pre-order where each unit that constitutes the partial pre-order is important and should be considered individually. To address this issue, in this paper, we study how a partial preorder representing the prior epistemic state can be revised by another partial pre-order (the new input) from a different perspective, where the revision is conducted recursively on the individual units of partial pre-orders. We propose different revision operators (rules), dubbed the extension, match, inner and outer revision operators, from different revision points of view. We also analyze several properties for these operators.