2,324 research outputs found
Exploiting Parallelism for Hard Problems in Abstract Argumentation
Abstract argumentation framework (AF) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and enumeration problems associated to AF s are missing, thus potentially limiting the efficacy of argumentation-based approaches in real domains. In this paper, we present an algorithm for enumerating the preferred extensions of abstract argumentation frameworks which exploits parallel computation. To this purpose, the SCC-recursive semantics definition schema is adopted, where extensions are defined at the level of specific sub-frameworks. The algorithm shows significant performance improvements in large frameworks, in terms of number of solutions found and speedup
Some Supplementaries to The Counting Semantics for Abstract Argumentation
Dung's abstract argumentation framework consists of a set of interacting
arguments and a series of semantics for evaluating them. Those semantics
partition the powerset of the set of arguments into two classes: extensions and
non-extensions. In order to reason with a specific semantics, one needs to take
a credulous or skeptical approach, i.e. an argument is eventually accepted, if
it is accepted in one or all extensions, respectively. In our previous work
\cite{ref-pu2015counting}, we have proposed a novel semantics, called
\emph{counting semantics}, which allows for a more fine-grained assessment to
arguments by counting the number of their respective attackers and defenders
based on argument graph and argument game. In this paper, we continue our
previous work by presenting some supplementaries about how to choose the
damaging factor for the counting semantics, and what relationships with some
existing approaches, such as Dung's classical semantics, generic gradual
valuations. Lastly, an axiomatic perspective on the ranking semantics induced
by our counting semantics are presented.Comment: 8 pages, 3 figures, ICTAI 201
Dynamics in Abstract Argumentation Frameworks with Recursive Attack and Support Relations
Argumentation is an important topic in the field of AI. There is a substantial amount of work about different aspects of Dung's abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are extending the framework to account for recursive attacks and supports, and considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects.We focus on Attack-Support Argumentation Frameworks (ASAFs) which allow for attack and support relations not only between arguments but also targeting attacks and supports at any level, and propose an approach for the incremental computation of extensions (sets of accepted arguments, attacks and supports) of updated ASAFs. Our approach assumes that an initial ASAF extension is given and uses it for first checking whether updates are irrelevant; for relevant updates, an extension of an updated ASAF is computed by translating the problem to the AF domain and leveraging on AF solvers. We experimentally show our incremental approach outperforms the direct computation of extensions for updated ASAFs.Fil: Alfano, Gianvincenzo. Universita Della Calabria.; ItaliaFil: Cohen, Andrea. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Ciencias e IngenierÃa de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e IngenierÃa de la Computación. Instituto de Ciencias e IngenierÃa de la Computación; ArgentinaFil: Gottifredi, Sebastian. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Ciencias e IngenierÃa de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e IngenierÃa de la Computación. Instituto de Ciencias e IngenierÃa de la Computación; ArgentinaFil: Greco, Sergio. Universita Della Calabria.; ItaliaFil: Parisi, Francesco. Universita Della Calabria.; ItaliaFil: Simari, Guillermo R.. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Ciencias e IngenierÃa de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e IngenierÃa de la Computación. Instituto de Ciencias e IngenierÃa de la Computación; Argentina24th European Conference on Artificial IntelligenceSantiago de CompostelaEspañaEuropean Association for Artificial IntelligenceUniversidad de Santiago de Compostel
Counting Complexity for Reasoning in Abstract Argumentation
In this paper, we consider counting and projected model counting of
extensions in abstract argumentation for various semantics. When asking for
projected counts we are interested in counting the number of extensions of a
given argumentation framework while multiple extensions that are identical when
restricted to the projected arguments count as only one projected extension. We
establish classical complexity results and parameterized complexity results
when the problems are parameterized by treewidth of the undirected
argumentation graph. To obtain upper bounds for counting projected extensions,
we introduce novel algorithms that exploit small treewidth of the undirected
argumentation graph of the input instance by dynamic programming (DP). Our
algorithms run in time double or triple exponential in the treewidth depending
on the considered semantics. Finally, we take the exponential time hypothesis
(ETH) into account and establish lower bounds of bounded treewidth algorithms
for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1
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