1,262 research outputs found

    On the equivalence between logic programming semantics and argumentation semantics

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    This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin

    Counting Complexity for Reasoning in Abstract Argumentation

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    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

    Enforcement in Abstract Argumentation via Boolean Optimization

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    Computational aspects of argumentation are a central research topic of modern artificial intelligence. A core formal model for argumentation, where the inner structure of arguments is abstracted away, was provided by Dung in the form of abstract argumentation frameworks (AFs). AFs are syntactically directed graphs with the nodes representing arguments and edges representing attacks between them. Given the AF, sets of jointly acceptable arguments or extensions are defined via different semantics. The computational complexity and algorithmic solutions to so-called static problems, such as the enumeration of extensions, is a well-studied topic. Since argumentation is a dynamic process, understanding the dynamic aspects of AFs is also important. However, computational aspects of dynamic problems have not been studied thoroughly. This work concentrates on different forms of enforcement, which is a core dynamic problem in the area of abstract argumentation. In this case, given an AF, one wants to modify it by adding and removing attacks in a way that a given set of arguments becomes an extension (extension enforcement) or that given arguments are credulously or skeptically accepted (status enforcement). In this thesis, the enforcement problem is viewed as a constrained optimization task where the change to the attack structure is minimized. The computational complexity of the extension and status enforcement problems is analyzed, showing that they are in the general case NP-hard optimization problems. Motivated by this, algorithms are presented based on the Boolean optimization paradigm of maximum satisfiability (MaxSAT) for the NP-complete variants, and counterexample-guided abstraction refinement (CEGAR) procedures, where an interplay between MaxSAT and Boolean satisfiability (SAT) solvers is utilized, for problems beyond NP. The algorithms are implemented in the open source software system Pakota, which is empirically evaluated on randomly generated enforcement instances

    Compact Argumentation Frameworks

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    Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.Comment: Contribution to the 15th International Workshop on Non-Monotonic Reasoning, 2014, Vienn

    Reasoning about Action: An Argumentation - Theoretic Approach

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    We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper
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