65 research outputs found
The Equational Approach to CF2 Semantics
We introduce a family of new equational semantics for argumentation networks
which can handle odd and even loops in a uniform manner. We offer one version
of equational semantics which is equivalent to CF2 semantics, and a better
version which gives the same results as traditional Dung semantics for even
loops but can still handle odd loops.Comment: 36 pages, version dated 15 February 201
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
The Principle-Based Approach to Abstract Argumentation Semantics
The principle-based or axiomatic approach is a methodology to choose an argumentation semantics for a particular application, and to guide the search for new argumentation semantics. This article gives a complete classification of the fifteen main alternatives for argumentation semantics using the twenty-seven main principles discussed in the literature on abstract argumentation, extending Baroni and Giacomin’s original classification with other semantics and principles proposed in the literature. It also lays the foundations for a study of representation and (im)possibility results for abstract argumentation, and for a principle-based approach for extended argumentation such as bipolar frameworks, preference-based frameworks, abstract dialectical frameworks, weighted frameworks, and input/output frameworks
Joint attacks and accrual in argumentation frameworks
While modelling arguments, it is often useful to represent joint attacks, i.e., cases where multiple arguments jointly attack another (note that this is different from the case where multiple arguments attack another in isolation). Based on this remark, the notion of joint attacks has been proposed as a useful extension of classical Abstract Argumentation Frameworks, and has been shown to constitute a genuine extension in terms of expressive power. In this chapter, we review various works considering the notion of joint attacks from various perspectives, including abstract and structured frameworks. Moreover, we present results detailing the relation among frameworks with joint attacks and classical argumentation frameworks, computational aspects, and applications of joint attacks. Last but not least, we propose a roadmap for future research on the subject, identifying gaps in current research and important research directions.Fil: Bikakis, Antonis. University College London; Estados UnidosFil: Cohen, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Dvoák, Wolfgang. Technische Universitat Wien; AustriaFil: Flouris, Giorgos. Foundation for Research and Technology; GreciaFil: Parsons, Simon. University of Lincoln; Reino Unid
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