17 research outputs found
Compact Argumentation Frameworks
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
Improved Answer-Set Programming Encodings for Abstract Argumentation
The 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.Comment: To appear in Theory and Practice of Logic Programming (TPLP),
Proceedings of ICLP 201
Defense semantics of argumentation: encoding reasons for accepting arguments
In this paper we show how the defense relation among abstract arguments can
be used to encode the reasons for accepting arguments. After introducing a
novel notion of defenses and defense graphs, we propose a defense semantics
together with a new notion of defense equivalence of argument graphs, and
compare defense equivalence with standard equivalence and strong equivalence,
respectively. Then, based on defense semantics, we define two kinds of reasons
for accepting arguments, i.e., direct reasons and root reasons, and a notion of
root equivalence of argument graphs. Finally, we show how the notion of root
equivalence can be used in argumentation summarization.Comment: 14 pages, first submitted on April 30, 2017; 16 pages, revised in
terms of the comments from MIREL2017 on August 03, 201
On the Relative Expressiveness of Argumentation Frameworks, Normal Logic Programs and Abstract Dialectical Frameworks
We analyse the expressiveness of the two-valued semantics of abstract
argumentation frameworks, normal logic programs and abstract dialectical
frameworks. By expressiveness we mean the ability to encode a desired set of
two-valued interpretations over a given propositional signature using only
atoms from that signature. While the computational complexity of the two-valued
model existence problem for all these languages is (almost) the same, we show
that the languages form a neat hierarchy with respect to their expressiveness.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014
Characterizing strongly admissible sets
The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility (in contrast to grounded semantics) ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable.</jats:p
Investigating subclasses of abstract dialectical frameworks
Dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes with the price of higher computational complexity, thus an understanding of potentially easier subclasses is essential. Compared to Dung argumentation frameworks, where several subclasses such as acyclic and symmetric frameworks are well understood, there has been no in-depth analysis for ADFs in such direction yet (with the notable exception of bipolar ADFs). In this work, we introduce certain subclasses of ADFs and investigate their properties. In particular, we show that for acyclic ADFs, the different semantics coincide. On the other hand, we show that the concept of symmetry is less powerful for ADFs and further restrictions are required to achieve results that are similar to the known ones for Dung's frameworks. A particular such subclass (support-free symmetric ADFs) turns out to be closely related to argumentation frameworks with collective attacks (SETAFs); we investigate this relation in detail and obtain as a by-product that even for SETAFs symmetry is less powerful than for AFs. We also discuss the role of odd-length cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures
On the Existence of Characterization Logics and Fundamental Properties of Argumentation Semantics
Given the large variety of existing logical formalisms it is of utmost importance
to select the most adequate one for a specific purpose, e.g. for representing
the knowledge relevant for a particular application or for using the formalism
as a modeling tool for problem solving. Awareness of the nature of a logical
formalism, in other words, of its fundamental intrinsic properties, is indispensable
and provides the basis of an informed choice.
One such intrinsic property of logic-based knowledge representation languages
is the context-dependency of pieces of knowledge. In classical propositional
logic, for example, there is no such context-dependence: whenever two
sets of formulas are equivalent in the sense of having the same models (ordinary
equivalence), then they are mutually replaceable in arbitrary contexts (strong
equivalence). However, a large number of commonly used formalisms are not
like classical logic which leads to a series of interesting developments. It turned
out that sometimes, to characterize strong equivalence in formalism L, we can
use ordinary equivalence in formalism L0: for example, strong equivalence in
normal logic programs under stable models can be characterized by the standard
semantics of the logic of here-and-there. Such results about the existence of
characterizing logics has rightly been recognized as important for the study of
concrete knowledge representation formalisms and raise a fundamental question:
Does every formalism have one? In this thesis, we answer this question
with a qualified “yes”. More precisely, we show that the important case of
considering only finite knowledge bases guarantees the existence of a canonical
characterizing formalism. Furthermore, we argue that those characterizing
formalisms can be seen as classical, monotonic logics which are uniquely determined (up to isomorphism) regarding their model theory.
The other main part of this thesis is devoted to argumentation semantics
which play the flagship role in Dung’s abstract argumentation theory. Almost
all of them are motivated by an easily understandable intuition of what should
be acceptable in the light of conflicts. However, although these intuitions equip
us with short and comprehensible formal definitions it turned out that their
intrinsic properties such as existence and uniqueness, expressibility, replaceability
and verifiability are not that easily accessible. We review the mentioned
properties for almost all semantics available in the literature. In doing so we
include two main axes: namely first, the distinction between extension-based
and labelling-based versions and secondly, the distinction of different kind of
argumentation frameworks such as finite or unrestricted ones