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Decision Problem
Polynomial Hierarchy
Quantified Boolean Formula
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Checking the acceptability of a set of arguments
Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas
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Reasoning in Argumentation Frameworks Using Quantified Boolean Formulas
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Reasoning in Argumentation Frameworks Using Quantified Boolean Formulas
(
Citations: 6
)
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Uwe Egly
,
Stefan Woltran
This paper describes a generic approach to implement propositional ar- gumentation frameworks by means of quantified Boolean formu las (QBFs). The motivation to this work is based on the following observations: Firstly, depending on the underlying deductive system and the chosen semantics (i.e., the kind of ex- tension under consideration), reasoning in argumentation frameworks can become computationally involving up to the fourth level of the polynomial hierarchy. This makes the language of QBFs a suitable target formalism since decision problems from the
polynomial hierarchy
can be efficiently represente d in terms of QBF. Sec- ondly, several practicably efficient solvers for QBFs are cu rrently available, and thus can be used as black-box engines in potential implementations of argumenta- tion frameworks. Finally, the definition of suitable QBF mod ules provides us with a tool box in order to capture a broad range of reasoning tasks associated to formal argumentation.
Conference:
Computational Models of Argument - COMMA
, pp. 133-144, 2006
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Citation Context
(3)
...In particular, comparisons with QBF encodings for other argumentation formulations [
22
] or, encodings in terms of classical logic for nonmonotonic formalisms in general [3, 19] are now enabled...
Philippe Besnard
,
et al.
Encoding deductive argumentation in quantified Boolean formulae
...On the other hand, though Egly et al. [
10
] showed a generic approach to implement Dung’s four argumentation semantics, their method is different from ours since it is represented in terms of QBFs (Quantified Boolean Formulas) instead of ASP, which coincides with the encodings to propositional logic given by Besnard and Doutre [1]...
Toshiko Wakaki
,
et al.
Computing Argumentation Semantics in Answer Set Programming
...Earlier work [7,
17
] proposed reductions for basic argumentation frameworks to (quantified) propositional logi c. In this work, we present solutions for reasoning problems in different types of argumentation frameworks by means of computing the answer sets of an (extended) datalog program...
...This is in contrast to, e.g., the reduct ions to (quantified) propositional logic [7,
17
], where one obtains a formula which completely depends on the AF to process...
UR INFORMATIONSSYSTEME
.
Answer-Set Programming Encodings for Argumentation Frameworks
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Citations: 21
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Ofer Arieli
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Marc Denecker
Journal:
Journal of Logic and Computation - LOGCOM
, vol. 13, no. 4, pp. 557-580, 2003
Checking the acceptability of a set of arguments
(
Citations: 11
)
Philippe Besnard
,
Sylvie Doutre
Conference:
Non-Monotonic Reasoning - NMR
, pp. 59-64, 2004
An Abstract, Argumentation-Theoretic Approach to Default Reasoning
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Andrei Bondarenko
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Phan Minh Dung
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Artificial Intelligence - AI
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Preferred Arguments are Harder to Compute than Stable Extension
(
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Yannis Dimopoulos
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Bernhard Nebel
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Francesca Toni
Conference:
International Joint Conference on Artificial Intelligence - IJCAI
, pp. 36-43, 1999
On the computational complexity of assumption-based argumentation for default reasoning
(
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)
Yannis Dimopoulos
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Bernhard Nebel
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Francesca Toni
Journal:
Artificial Intelligence - AI
, vol. 141, no. 1/2, pp. 57-78, 2002
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Citations
(6)
Answer-set programming encodings for argumentation frameworks
(
Citations: 3
)
Uwe Egly
,
Sarah Alice Gaggl
,
Stefan Woltran
Journal:
Argument & Computation
, vol. 1, no. 2, pp. 147-177, 2010
Encoding deductive argumentation in quantified Boolean formulae
(
Citations: 3
)
Philippe Besnard
,
Anthony Hunter
,
Stefan Woltran
Journal:
Artificial Intelligence - AI
, vol. 173, no. 15, pp. 1406-1423, 2009
Computing Argumentation Semantics in Answer Set Programming
(
Citations: 3
)
Toshiko Wakaki
,
Katsumi Nitta
Conference:
JSAI Workshops
, pp. 254-269, 2008
An Overview of Argumentation Semantics Una Revisión de las Semánticas de Argumentación
Juan Carlos Nieves
,
Mauricio Osorio
,
Ulises Cortés
Answer-Set Programming Encodings for Argumentation Frameworks
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