scholarly journals Reasoning over Assumption-Based Argumentation Frameworks via Direct Answer Set Programming Encodings

2019 ◽  
Vol 33 ◽  
pp. 2938-2945 ◽  
Author(s):  
Tuomo Lehtonen ◽  
Johannes P. Wallner ◽  
Matti Järvisalo
Keyword(s):  
Answer Set Programming ◽  
Direct Approach ◽  
Problem Complexity ◽  
New Approach ◽  
Abstract Argumentation ◽  
Reasoning Systems ◽  
Complexity Results ◽  
Empirical Performance ◽  
Direct Answer ◽  
Answer Set

Focusing on assumption-based argumentation (ABA) as a central structured formalism to AI argumentation, we propose a new approach to reasoning in ABA with and without preferences. While previous approaches apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct approach by encoding ABA reasoning tasks in answer set programming. This significantly improves on the empirical performance of current ABA reasoning systems. We also give new complexity results for reasoning in ABA+, suggesting that the integration of preferential information into ABA results in increased problem complexity for several central argumentation semantics.

scholarly journals Declarative Algorithms and Complexity Results for Assumption-Based Argumentation

2021 ◽  
Vol 71 ◽  
pp. 265-318
Author(s):  
Tuomo Lehtonen ◽  
Johannes P. Wallner ◽  
Matti Järvisalo
Keyword(s):  
Computational Models ◽  
Empirical Evaluation ◽  
Knowledge Representation And Reasoning ◽  
Problem Complexity ◽  
Intrinsic Structure ◽  
New Approach ◽  
Reasoning Systems ◽  
Algorithms And Complexity ◽  
Empirical Performance ◽  
Structured Argumentation

The study of computational models for argumentation is a vibrant area of artificial intelligence and, in particular, knowledge representation and reasoning research. Arguments most often have an intrinsic structure made explicit through derivations from more basic structures. Computational models for structured argumentation enable making the internal structure of arguments explicit. Assumption-based argumentation (ABA) is a central structured formalism for argumentation in AI. In this article, we make both algorithmic and complexity-theoretic advances in the study of ABA. In terms of algorithms, we propose a new approach to reasoning in a commonly studied fragment of ABA (namely the logic programming fragment) with and without preferences. While previous approaches to reasoning over ABA frameworks apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct declarative approach to ABA reasoning by encoding ABA reasoning tasks in answer set programming. We show via an extensive empirical evaluation that our approach significantly improves on the empirical performance of current ABA reasoning systems. In terms of computational complexity, while the complexity of reasoning over ABA frameworks is well-understood, the complexity of reasoning in the ABA+ formalism integrating preferences into ABA is currently not fully established. Towards bridging this gap, our results suggest that the integration of preferential information into ABA via so-called reverse attacks results in increased problem complexity for several central argumentation semantics.

Complexity results for probabilistic answer set programming

2020 ◽  
Vol 118 ◽  
pp. 133-154 ◽  
Author(s):  
Denis Deratani Mauá ◽  
Fabio Gagliardi Cozman
Keyword(s):  
Answer Set Programming ◽  
Complexity Results ◽  
Answer Set

scholarly journals Complexity results for answer set programming with bounded predicate arities and implications

2007 ◽  
Vol 51 (2-4) ◽  
pp. 123-165 ◽  
Author(s):  
Thomas Eiter ◽  
Wolfgang Faber ◽  
Michael Fink ◽  
Stefan Woltran
Keyword(s):  
Answer Set Programming ◽  
Complexity Results ◽  
Answer Set

scholarly journals Improved answer-set programming encodings for abstract argumentation

2015 ◽  
Vol 15 (4-5) ◽  
pp. 434-448 ◽  
Author(s):  
SARAH A. GAGGL ◽  
NORBERT MANTHEY ◽  
ALESSANDRO RONCA ◽  
JOHANNES P. WALLNER ◽  
STEFAN WOLTRAN
Keyword(s):  
Answer Set Programming ◽  
Efficient Solutions ◽  
Crucial Step ◽  
Abstract Argumentation ◽  
Argumentation Systems ◽  
Answer Set

AbstractThe design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor. In this paper, we present new encodings for three prominent argumentation semantics using the concept of conditional literals in disjunctions as provided by the ASP-system clingo. Our new encodings are not only more succinct than previous versions, but also outperform them on standard benchmarks.

scholarly journals A translational approach to constraint answer set solving

2010 ◽  
Vol 10 (4-6) ◽  
pp. 465-480 ◽  
Author(s):  
CHRISTIAN DRESCHER ◽  
TOBY WALSH
Keyword(s):  
Answer Set Programming ◽  
Constraint Satisfaction Problems ◽  
Logic Programs ◽  
New Approach ◽  
Constraint Processing ◽  
Translational Approach ◽  
Unit Propagation ◽  
Processing Techniques ◽  
Finite Domains ◽  
Answer Set

AbstractWe present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be decomposed into logic programs such that unit-propagation achieves arc, bound or range consistency. Experiments with our encodings demonstrate their computational impact.

scholarly journals A Semantic Characterization ASP Base Revision

2019 ◽  
Vol 66 ◽  
pp. 989-1029
Author(s):  
Laurent Garcia ◽  
Claire Lefèvre ◽  
Igor Stéphan ◽  
Odile Papini ◽  
Éric Würbel
Keyword(s):  
Classical Logic ◽  
Answer Set Programming ◽  
Semantic Content ◽  
Logic Programs ◽  
Rule Based ◽  
Complexity Results ◽  
Base Revision ◽  
Answer Sets ◽  
Answer Set

The paper deals with base revision for Answer Set Programming (ASP). Base revision in classical logic is done by the removal of formulas. Exploiting the non-monotonicity of ASP allows one to propose other revision strategies, namely addition strategy or removal and/or addition strategy. These strategies allow one to define families of rule-based revision operators. The paper presents a semantic characterization of these families of revision operators in terms of answer sets. This semantic characterization allows for equivalently considering the evolution of syntactic logic programs and the evolution of their semantic content. It then studies the logical properties of the proposed operators and gives complexity results.  

scholarly journals Solving Advanced Argumentation Problems with Answer Set Programming

2020 ◽  
Vol 20 (3) ◽  
pp. 391-431
Author(s):  
GERHARD BREWKA ◽  
MARTIN DILLER ◽  
GEORG HEISSENBERGER ◽  
THOMAS LINSBICHLER ◽  
STEFAN WOLTRAN
Keyword(s):  
Answer Set Programming ◽  
Polynomial Hierarchy ◽  
Abstract Argumentation ◽  
The Third ◽  
Labeled Graphs ◽  
The Relationship ◽  
Answer Set

AbstractPowerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete, and preferred semantics.

scholarly journals Debugging Non-ground ASP Programs: Technique and Graphical Tools

2019 ◽  
Vol 19 (2) ◽  
pp. 290-316 ◽  
Author(s):  
CARMINE DODARO ◽  
PHILIP GASTEIGER ◽  
KRISTIAN REALE ◽  
FRANCESCO RICCA ◽  
KONSTANTIN SCHEKOTIHIN
Keyword(s):  
Answer Set Programming ◽  
Declarative Programming ◽  
Graphical Interface ◽  
Development Environment ◽  
Integrated Development ◽  
New Approach ◽  
Meta Programming ◽  
User Friendly ◽  
Programming Paradigms ◽  
Answer Set

AbstractAnswer set programming (ASP) is one of the major declarative programming paradigms in the area of logic programming and non-monotonic reasoning. Despite that ASP features a simple syntax and an intuitive semantics, errors are common during the development of ASP programs. In this paper we propose a novel debugging approach allowing for interactive localization of bugs in non-ground programs. The new approach points the user directly to a set of non-ground rules involved in the bug, which might be refined (up to the point in which the bug is easily identified) by asking the programmer a sequence of questions on an expected answer set. The approach has been implemented on top of the ASP solver wasp. The resulting debugger has been complemented by a user-friendly graphical interface, and integrated in aspide, a rich integrated development environment (IDE) for answer set programs. In addition, an empirical analysis shows that the new debugger is not affected by the grounding blowup limiting the application of previous approaches based on meta-programming.

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