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Argumentation for Decision making: A simple scenario.
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Following the argumentation framework and semantics proposed by Dung, we are interested in the problem of deciding which set of acceptable arguments support the decision making in an agent-based platform called CARREL. It is an agent-agency which mediates organ transplants. We present two possible ways to infer the stable and preferred extensions o...
Citations
... It is not immediately clear, for example, if and how it captures Dung's abstract argumentation frameworks (AFs) [9], another important AI formalism whose strong equivalence has been studied in the recent past [10,11]. More precisely, while AFs with all their semantics [13,14,12]. However, the AF where both b and c attack a (the union of the two AFs above) corresponds to the logic program P 3 = {a ← ∼b, ∼c}, where obviously the three programs are not subset-related: 1 As an AF is a pair (A, R) with A a set of arguments and R ⊆ A × A an attack relation, the union of AFs is defined component-wise: (A 1 , R 1 )∪ (A 2 , R 2 ) = (A 1 ∪ A 2 , R 1 ∪ R 2 ). ...
Two knowledge bases are strongly equivalent if and only if they are mutually interchangeable in arbitrary contexts. This notion is of high interest for any logical formalism, since it allows to locally replace parts of a given theory without changing its meaning. In contrast to classical logic, where strong equivalence coincides with standard equivalence (having the same models), it is possible to find ordinary but not strongly equivalent objects for any nonmonotonic formalism available in the literature. Consequently, much effort has been devoted to characterizing strong equivalence for knowledge representation formalisms such as logic programs under the stable model semantics, Reiter's default logic, or Dung's argumentation frameworks. For example, strong equivalence for logic programs under stable models can be characterized by so-called HT-models. More precisely, two logic programs are strongly equivalent if and only if they are standard equivalent in the logic of here and there. This means, the logic of here and there can be seen as a characterizing formalism for logic programs under stable model semantics.
The aim of this article is to study whether the existence of such characterization logics can be guaranteed for any logic. One main result is that every knowledge representation formalism that allows for a notion of strong equivalence on its finite knowledge bases also possesses a canonical characterizing formalism. In particular, we argue that those characterizing formalisms can be seen as classical, monotonic logics. Moreover, we will not only show the existence of characterizing formalism, but even that the model theory of any characterizing logic is uniquely determined (up to isomorphism).
... Thus although AFs are essentially a restricted subclass of normal logic programs with respect to the ordinary equivalence of having the same models, this does not carry over to strong equivalence because the respective notions of knowledge base union are different in AFs and normal logic programs. For example, the AF where b attacks a corresponds to the logic program P 1 = {a ← ∼b}; likewise, P 2 = {a ← ∼c} corresponds to the AF where c attacks a [Osorio et al., 2005;Wu et al., 2009;. However, the AF where both b and c attack a (the union of the two AFs above) corresponds to the logic program P 3 = {a ← ∼b, ∼c}, where obviously the three programs are not subset-related: P 1 ⊆ P 3 and P 2 ⊆ P 3 . ...
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. In this treatise we consider the existence characterization logics as well as properties like existence and uniqueness, expressibility, replaceability and verifiability in the realm of abstract argumentation
... Thus although AFs are essentially a restricted subclass of normal logic programs with respect to the ordinary equivalence of having the same models, this does not carry over to strong equivalence because the respective notions of knowledge base union are different in AFs and normal logic programs. For example, the AF where b attacks a corresponds to the logic program P 1 = {a ← ∼b}; likewise, P 2 = {a ← ∼c} corresponds to the AF where c attacks a [Osorio et al., 2005;Wu et al., 2009;. However, the AF where both b and c attack a (the union of the two AFs above) corresponds to the logic program P 3 = {a ← ∼b, ∼c}, where obviously the three programs are not subset-related: P 1 ⊆ P 3 and P 2 ⊆ P 3 . ...
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 L': 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.
... Thus although AFs are essentially a restricted subclass of normal logic programs with respect to the ordinary equivalence of having the same models, this does not carry over to strong equivalence because the respective notions of knowledge base union are different in AFs and 75 normal logic programs. For example, the AF where b attacks a corresponds to the logic program P 1 = {a ← ∼b}; likewise, P 2 = {a ← ∼c} corresponds to the AF where c attacks a [13,14,12]. However, the AF where both b and c attack a (the union of the two AFs above) corresponds to the logic program P 3 = {a ← ∼b, ∼c}, where obviously the three programs are not subset-related: 80 P 1 ⊆ P 3 and P 2 ⊆ P 3 . ...
Two knowledge bases are strongly equivalent if and only if they are mutually interchangeable in arbitrary contexts. This notion is of high interest for any logical formalism since it allows one to locally replace, and thus give rise for simplification , parts of a given theory without changing the semantics of the latter. In contrast to classical logic where strong equivalence coincides with standard equivalence (having the same models), it is possible to find ordinary but not strongly equivalent objects for any nonmonotonic formalism available in the literature. Consequently, much effort has been devoted to characterizing strong equivalence for knowledge representation formalisms such as logic programs, Re-iter's default logic, or Dung's argumentation frameworks. For example, strong equivalence for logic programs under stable models can be characterized by so-called HT-models. More precisely, two logic programs are strongly equivalent if and only if they are standard equivalent in the logic here-and-there. This means, the logic of here-and-there can be seen as a characterizing formalism for logic programs under stable model semantics. The aim of this article is to study whether the existence of such characterization logics can be guaranteed for any logic. One main result is that every knowledge representation formalism that allows for a notion of strong equivalence on its finite knowledge bases also possesses a canonical characterizing formalism. In particular, we argue that those characterizing formalisms can be seen as classical, monotonic logics. Moreover, we will not only show the existence of characterizing formalism, but even that the model theory of any characterizing logic is uniquely determined (up to isomorphism).
... In Osorio et al. (2005), the authors propose the use of ASP and of the argumentation framework proposed by Dung (1995) to represent a medical transplantation knowledge base. They define CARREL-ASP, namely CARREL Cortés et al. (2005) extended with ASP, to perform decision making based on argumentation framework. ...
In this paper, we discuss the potential role of answer set programming (ASP) in the context of approaches to the development of agents and multi-agent systems especially in the realm of Computational Logic. After shortly recalling the main (computational-logic-based) agent-oriented frameworks, we introduce ASP; then, we discuss the usefulness of a potential integration of the two paradigms in a modular heterogeneous framework, and the feasibility of such integration. This also in the more general view of improving and empowering flexibility of agent-oriented frameworks. Relevant literature will be mentioned and discussed. Possible future directions and potential developments will be outlined.
... Correspondence under certain semantics between an ABA framework and some translation into a logic program is not surprising since existing translations from ABA to AA (Dung et al., 2007;Caminada et al., 2015b;Schulz & Toni, 2017) and from AA to LP (Osorio, Zepeda, Nieves, & Cortés, 2005;Wu, Caminada, & Gabbay, 2009;Strass, 2013;Caminada, Sá, Alcântara, & Dvořák, 2015a) can be used to show correspondence under certain semantics between an ABA framework and the logic program resulting from concatenation. However, the concatenation may lead to an exponential blow-up as it requires the construction of all arguments from an ABA framework and is therefore not suitable for practical matters such as the computation of ABA semantics using LP tools. ...
... As pointed out in the introduction, it is not surprising that there exists a semantic correspondence for some translation from an ABA framework into a logic program due to the semantic correspondence of ABA and AA (Dung et al., 2007;Caminada et al., 2015b;Schulz & Toni, 2017) and AA and LP (Osorio et al., 2005;Wu et al., 2009;Strass, 2013;Caminada et al., 2015a). However, the translation obtained from concatenating the ABA to AA and the AA to LP translations is different from our translation, as illustrated in the following. ...
... Translating F into an AA framework and then into a logic program using existing translations (Dung et al., 2007;Caminada et al., 2015b;Schulz & Toni, 2017;Osorio et al., 2005;Wu et al., 2009;Strass, 2013;Caminada et al., 2015a) yields the logic program P = {x ← ; y ← ; z ← not y ; v ← ; w ← not y} (where the names of the atoms could be anything) 10 . In comparison, according to our translation we obtain the logic program P F = {a ← ; b ← a, not d ; c ← a, not b}, which is much closer to the underlying ABA framework. ...
Assumption-Based Argumentation (ABA) has been shown to subsume various other non-monotonic reasoning formalisms, among them normal logic programming (LP). We re-examine the relationship between ABA and LP and show that normal LP also subsumes (flat) ABA. More precisely, we specify a procedure that given a (flat) ABA framework yields an associated logic program with almost the same syntax whose semantics coincide with those of the ABA framework. That is, the 3-valued stable (respectively well-founded, regular, 2-valued stable, and ideal) models of the associated logic program coincide with the complete (respectively grounded, preferred, stable, and ideal) assumption labellings and extensions of the ABA framework. Moreover, we show how our results on the translation from ABA to LP can be reapplied for a reverse translation from LP to ABA, and observe that some of the existing results in the literature are in fact special cases of our work. Overall, we show that (flat) ABA frameworks can be seen as normal logic programs with a slightly different syntax. This implies that methods developed for one of these formalisms can be equivalently applied to the other by simply modifying the syntax.
... Dung showed that argumentation can be viewed as logic programming with negation as failure and vice versa. This strong relationship between argumentation and logic programming has given way to intensive research in order to explore the relationship between argumentation and logic programming (Caminada et al. 2013;Carballido et al. 2009;Dung 1995;Nieves et al. 2005;Nieves et al. 2008;Osorio et al. 2013;Nieves et al. 2011;Strass 2013;Wu et al. 2009). A basic requirement for exploring the relationship between argumentation and logic programming is to identify proper mappings which allow us to transform an argumentation framework into a logic program and vice versa. ...
... It is well-known that the computational complexity of the decision problems of argumentation semantics ranges from NP-complete to Π (p) 2 -complete. In this setting, Answer Set Programming has consolidated as a strong approach for building argumentation-based systems (Charwat et al. 2015;Egly et al. 2010;Toni and Sergot 2011;Nieves et al. 2005). ...
Characterizations of semi-stable and stage extensions in terms of two-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming counterparts of the notion of range which is an established concept in argumentation semantics.
... The translation chain from AFs to ADFs to LPs is compact, and faithful for AF stable semantics and LP stable semantics (Osorio, Zepeda, Nieves, & Cortés, 2005), and AF stable semantics and LP supported semantics (Strass, 2013). It is size-preserving since the single rule for each atom contains all attackers once: ...
We analyse the expressiveness of Brewka and Woltran's abstract dialectical frameworks for two-valued semantics. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. We also compare ADFs' expressiveness with that of (the two-valued semantics of) abstract argumentation frameworks, normal logic programs and propositional logic. 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. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements. We finally also analyse and compare the representational succinctness of ADFs (for two-valued model semantics), that is, their capability to represent two-valued interpretation sets in a space-efficient manner.
... It is a consequence of Lemma 3.14 in (Strass 2013) that this translation preserves the supported model semantics. From AFs to LPs The translation chain from AFs to ADFs to LPs is compact, and faithful for AF stable semantics and LP stable semantics (Osorio et al. 2005), and AF stable semantics and LP supported semantics (Strass 2013). From LPs to PL It is well-known that logic programs under supported model semantics can be translated to propositional logic (Clark 1978). ...
We analyze the relative 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 vocabulary A using only atoms from A. 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. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements.
... Naturally, reduction-based methods can be distinguished by the target system. Many such approaches have been studied for abstract argumentation ranging from propositional logic [19,18,21,20], constraint satisfaction problems (CSP) [27,23,26,28] and answer-set programming (ASP) [30,[74][75][76] to equational systems [32,77]. We will give an overview of these approaches and in particular focus on the first three very prominent target systems, the reductions to propositional logic, CSP and ASP. ...
Within the last decade, abstract argumentation has emerged as a central field in Artificial Intelligence. Besides providing a core formalism for many advanced argumentation systems, abstract argumentation has also served to capture several non-monotonic logics and other AI related principles. Although the idea of abstract argumentation is appealingly simple, several reasoning problems in this formalism exhibit high computational complexity. This calls for advanced techniques when it comes to implementation issues, a challenge which has been recently faced from different angles. In this survey, we give an overview on different methods for solving reasoning problems in abstract argumentation and compare their particular features. Moreover, we highlight available state-of-the-art systems for abstract argumentation, which put these methods to practice.
