Aggregated Fuzzy Answer Set Programming

Fuzzy Answer Set programming (FASP) is an extension of answer set programming
(ASP), based on fuzzy logic. It allows to encode continuous optimization
problems in the same concise manner as ASP allows to model combinatorial problems.
As a result of its inherent continuity, rules in FASP may be satised or violated to
certain degrees. Rather than insisting that all rules are fully satised, we may only
require that they are satised partially, to the best extent possible. However, most approaches
that feature partial rule satisfaction limit themselves to attaching predened
weights to rules, which is not suciently
exible for most real-life applications. In this
paper, we develop an alternative, based on aggregator functions that specify which
(combination of) rules are most important to satisfy. We extend upon previous work
by allowing aggregator expressions to dene partially ordered preferences, and by the
use of a xpoint semantics.