Preferred answer sets for extended logic programs

Abstract

In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities to rules is not new, and has been explored in different contexts. However, we show that many approaches to priority handling, most of which are inherited from closely related formalisms like default logic, are not suitable and fail on intuitive examples. Our approach, which obeys abstract, general principles that any approach to prioritized knowledge representation should satisfy, handles them in the expected way. Moreover, we investigate the complexity of our approach. It appears that strong preference on answer sets does not add on the complexity of the principal reasoning tasks, and weak preference leads only to a mild increase in complexity.

Querying with Intrinsic Preferences

“…The work on prioritized logic programming and nonmonotonic reasoning [5,6,21] has potential applications to databases. However, like [11] it relies on specialized evaluation mechanisms.…”

“…It encompasses preference logics [23,19,13], preference reasoning [24,22,4], prioritized nonmonotonic reasoning and logic programming [5,6,21] and decision theory [7,8] (the list is by no means exhaustive). However, only a few papers [18,3,11,2,14,17] address the issue of user preferences in the context of database queries.…”

Using methods of declarative logic programming for intelligent information agents

“…In , an integrated framework combining updates and preferences is introduced, based on DynLP and the preference semantics due to Brewka and Eiter (1999). In this approach, a new language is defined, modeling sequences of programs P 1 , .…”

“…Formally, the notions of unsupported and unpreferred rules are introduced, in order to obtain the appropriate definition of the preferred stable models. The definition of preferred stable models is equivalent to the one of preferred answer sets given in (Brewka & Eiter, 1999).…”

Hierarchical Decision Making by Autonomous Agents

“…We can identify two directions for these preferences relations on programs. On the one hand, we can equip a logic program with a preference relation on the rules [18, 17, 15,10,7,5,27,1,22], while on the other hand we can consider a preference relation on the (extended) literals in the program: [21] proposes explicit preferences while [4,6] encodes dynamic preferences within the program.…”