A Classification and Survey of Preference Handling Approaches in Nonmonotonic Reasoning

Abstract

In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles.

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

“…In some sense, the use of such preferences among rules is related to using certainty weights, although the resulting semantics are closer in spirit to the approach from [3] than to the semantics we have developed throughout this paper. Quite a number of other works also deal with preference handling in non-monotonic reasoning; we refer to [36] for a thorough overview. Weak constraints [37] are yet another example of a problem that can be seen as a problem of preferences amongst rules.…”

HEX-Programs with Nested Program Calls

“…user-defined preference rules, and used for filtering as well as ranking results (cf. [4]): a host program selects appropriate candidates produced by a subprogram, using preference rules. The latter can be elegantly implemented as ordinary integrity constraints (for filtering), or as rules (possibly involving further external calls) to derive a rank.…”

Logic Programming with Defaults and Argumentation Theories

“…We say that an argumentation theory belongs to the AT C family if it includes the rules (5), (9), and (12)- (14); plus either (6) or (7) or (8); and either (10) or (11). Let AT be an argumentation theory in AT C and let the compatibility requirement be as follows.…”

“…Consider AT GCLP and a compatible lpda P. Let P ′ be the program obtained from P using the GCLP transformation of [19]. 9 Then the restrictions of the well-founded models of (P, AT GCLP ) and of P ′ to the predicates mentioned in P coincide.…”

“…Due to the sheer size of the literature on defeasible reasoning, it is not feasible to do justice to all prior work in this section. Therefore, we will focus on the more closely related work and refer the reader to a recent survey [9] for a broader discussion of the literature, including the works that we were unable to mention.…”