86,570 research outputs found
Empirical Evaluation of Abstract Argumentation: Supporting the Need for Bipolar and Probabilistic Approaches
In dialogical argumentation it is often assumed that the involved parties
always correctly identify the intended statements posited by each other,
realize all of the associated relations, conform to the three acceptability
states (accepted, rejected, undecided), adjust their views when new and correct
information comes in, and that a framework handling only attack relations is
sufficient to represent their opinions. Although it is natural to make these
assumptions as a starting point for further research, removing them or even
acknowledging that such removal should happen is more challenging for some of
these concepts than for others. Probabilistic argumentation is one of the
approaches that can be harnessed for more accurate user modelling. The
epistemic approach allows us to represent how much a given argument is believed
by a given person, offering us the possibility to express more than just three
agreement states. It is equipped with a wide range of postulates, including
those that do not make any restrictions concerning how initial arguments should
be viewed, thus potentially being more adequate for handling beliefs of the
people that have not fully disclosed their opinions in comparison to Dung's
semantics. The constellation approach can be used to represent the views of
different people concerning the structure of the framework we are dealing with,
including cases in which not all relations are acknowledged or when they are
seen differently than intended. Finally, bipolar argumentation frameworks can
be used to express both positive and negative relations between arguments. In
this paper we describe the results of an experiment in which participants
judged dialogues in terms of agreement and structure. We compare our findings
with the aforementioned assumptions as well as with the constellation and
epistemic approaches to probabilistic argumentation and bipolar argumentation
Conflict-Free Coloring Made Stronger
In FOCS 2002, Even et al. showed that any set of discs in the plane can
be Conflict-Free colored with a total of at most colors. That is,
it can be colored with colors such that for any (covered) point
there is some disc whose color is distinct from all other colors of discs
containing . They also showed that this bound is asymptotically tight. In
this paper we prove the following stronger results:
\begin{enumerate} \item [(i)] Any set of discs in the plane can be
colored with a total of at most colors such that (a) for any
point that is covered by at least discs, there are at least
distinct discs each of which is colored by a color distinct from all other
discs containing and (b) for any point covered by at most discs,
all discs covering are colored distinctively. We call such a coloring a
{\em -Strong Conflict-Free} coloring. We extend this result to pseudo-discs
and arbitrary regions with linear union-complexity.
\item [(ii)] More generally, for families of simple closed Jordan regions
with union-complexity bounded by , we prove that there exists
a -Strong Conflict-Free coloring with at most colors.
\item [(iii)] We prove that any set of axis-parallel rectangles can be
-Strong Conflict-Free colored with at most colors.
\item [(iv)] We provide a general framework for -Strong Conflict-Free
coloring arbitrary hypergraphs. This framework relates the notion of -Strong
Conflict-Free coloring and the recently studied notion of -colorful
coloring. \end{enumerate}
All of our proofs are constructive. That is, there exist polynomial time
algorithms for computing such colorings
New mathematical structures in renormalizable quantum field theories
Computations in renormalizable perturbative quantum field theories reveal
mathematical structures which go way beyond the formal structure which is
usually taken as underlying quantum field theory. We review these new
structures and the role they can play in future developments.Comment: 26p,4figs., Invited Contribution to Annals of Physics, minor typos
correcte
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