The Hardness of Revising Defeasible Preferences

Abstract

Non-monotonic reasoning typically deals with three kinds of knowledge. Facts are meant to describe immutable statements of the environment. Rules define relationships among elements. Lastly, an ordering among the rules, in the form of a superiority relation, establishes the relative strength of rules. To revise a non-monotonic theory, we can change either one of these three elements. We prove that the problem of revising a non-monotonic theory by only changing the superiority relation is a NP-complete problem.NICTA is funded by the Australian Government as represented by the Department of Communications and the Australian Research Council through the ICT Centre of Excellence program.

Non-monotonic Collective Decisions

“…Comparing this problem to other ones analogously defined, as in [12,11], we can prove the statement in Theorem 1. In the following, when referring to the problem of revising preference in a defeasible theory to derive one literal, we name this problem the Preference Revision Problem.…”

“It Could Be Worse, It Could Be Raining”: Reliable Automatic Meteorological Forecasting for Holiday Planning

“…-----------+------------+-----------------+-----------------+-----------------+-----------------+-----------------+-------------+---- -----------+------------+-----------------+-----------------+-----------------+-----------------+-----------------+-------------+---- Since the pioneering studies [5,9,23] and further engineering investigations on the commercial solutions [24], a first attempt going in the same direction that we following in this paper appeared in the 1990s [13] and inspired many specialized studies [19,21,17,12,4,20,10,11]. The ontological approach and the usage of the Internet of Things have been applied to forecasting quite recently [1,18] and we acknowledge that the main technical inspirations of our framework trace back these works, whereas the main influences come from the usage of non-monotonic deduction systems for sensor-based applications (clearly related to the initial part of the forecasting process) [28,8], and non-monotonic reasoning [16,25,14,15].…”

“…In this section, we develop a logical framework called MeteoLOG, that formalizes the hybrid reasoning at the basis of meteorological forecasting. MeteoLOG, informally introduced in [6], benefits from three standard logical approaches: defeasible logic [15], labeled deduction systems [22,29,30,7] and fuzzy/non-deterministic/probabilistic frameworks [10,2]. We introduce the syntax of formulae and of labels, along with a notion of prevalence, which imports a defeasible flavour into the system.…”