Semantics For Argumentation Frameworks Research Articles

Extension-based semantics for incomplete argumentation frameworks: properties, complexity and algorithms

AbstractIncomplete Argumentation Frameworks (IAFs) have been defined to incorporate some qualitative uncertainty in abstract argumentation: information such as ‘I am not sure whether this argument exists’ or ‘I am not sure whether this argument attacks that one’ can be expressed. Reasoning with IAFs is classically based on a set of completions, i.e. standard argumentation frameworks (AFs) that represent the possible worlds encoded in the IAF. The number of these completions may be exponential with respect to the number of arguments in the IAF. This leads, in some cases, to an increase of the complexity of reasoning, compared to the complexity of standard AFs. In this paper, we follow an approach that was initiated for Partial Argumentation Frameworks (PAFs) (a subclass of IAFs), which consists in defining new forms of conflict-freeness and defense, the properties that underly the definition of Dung’s semantics for AFs. We generalize these semantics from PAFs to IAFs. We show that, among three possible types of admissibility, only two of them satisfy some desirable properties. We use them to define two new families of extension-based semantics. We study the properties of these semantics, and in particular, we show that their complexity remains the same as in the case of Dung’s AFs. Finally, we propose a logical encoding of these semantics, and we show experimentally that this encoding can be used efficiently to reason with IAFs, thanks to the power of modern SAT solvers.

Reconstructing Arguments from Noisy Text

Social media are of paramount importance to public discourse. RANT aims to contribute methods and formalisms for extracting, representing, and processing arguments from noisy text found in social media discussions, using a large corpus of pre-referendum Brexit tweets as a running case study. We identify recurring linguistic argumentation patterns in a corpus-linguistic analysis and formulate corresponding corpus queries to extract arguments automatically. Given the huge amount of social media data available, our approach aims at high precision at the possible price of low recall. Argumentation patterns are directly associated with logical patterns in a dedicated formalism and accordingly, individual arguments are directly parsed as logical formulae. The logical formalism for argument representation features a broad range of modalities capturing real-life modes of expression. We cast this formalism as a family of instance logics in the generic framework of coalgebraic logic and complement it by a flexible framework to represent relationships between arguments; including standard relations like attack and support but also relations extracted from metadata. Some relations are inferred from the logical content of individual arguments. We are in the process of developing suitable generalizations of various extension semantics for argumentation frameworks combined with corresponding algorithmic methods to allow for the automated retrieval of large-scale argumentative positions.

Argumentation Reasoning via Circumscription with Pyglaf

The fundamental mechanism that humans use in argumentation can be formalized in abstract argumentation frameworks. Many semantics are associated with abstract argumentation frameworks, each one consisting of a set of extensions, that is, a set of sets of arguments. Some of these semantics are based on preference relations that essentially impose to maximize or minimize some property. This paper presents the argumentation reasoner PYGLAF, which provides a uniform view of many semantics for abstract argumentation frameworks in terms of circumscription. Specifically, several computational problems of abstract argumentation frameworks are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Finally, grounded extensions are obtained in polynomial time by unit propagation, and acceptance problems are addressed by first checking cardinality optimal models of circumscribed theories, so that the naive extension enumeration is possibly avoided.

On the responsibility for undecisiveness in preferred and stable labellings in abstract argumentation

Different semantics of abstract Argumentation Frameworks (AFs) provide different levels of decisiveness for reasoning about the acceptability of conflicting arguments. The stable semantics is useful for applications requiring a high level of decisiveness, as it assigns to each argument the label “accepted” or the label “rejected”. Unfortunately, stable labellings are not guaranteed to exist, thus raising the question as to which parts of AFs are responsible for the non-existence. In this paper, we address this question by investigating a more general question concerning preferred labellings (which may be less decisive than stable labellings but are always guaranteed to exist), namely why a given preferred labelling may not be stable and thus undecided on some arguments. In particular, (1) we give various characterisations of parts of an AF, based on the given preferred labelling, and (2) we show that these parts are indeed responsible for the undecisiveness if the preferred labelling is not stable. We then use these characterisations to explain the non-existence of stable labellings. We present two types of characterisations, based on labellings that are more (or equally) committed than the given preferred labelling on the one hand, and based on the structure of the given AF on the other, and compare the respective AF parts deemed responsible. To prove that our characterisations indeed yield responsible parts, we use a notion of enforcement of labels through structural revision, by means of which the preferred labelling of the given AF can be turned into a stable labelling of the structurally revised AF. Rather than prescribing how this structural revision is carried out, we focus on the enforcement of labels and leave the engineering of the revision open to fulfil differing requirements of applications and information available to users.

Representing Argumentation Frameworks in Answer Set Programming

This paper studies representation of argumentation frameworks (AFs) in answer set programming (ASP). Four different transformations from AFs to logic programs are provided under the complete semantics, stable semantics, grounded semantics and preferred semantics. The proposed transformations encode labelling-based argumentation semantics at the object level, and different semantics of AFs are uniformly characterized by stable models of transformed programs. We show how transformed programs can be used for solving AF problems such as query-answering, enforcement of arguments, and agreement of different AFs. The results exploit new connection between AF and logic programming, and enables one to realize AF on top of existing answer set solvers.

On the acceptance of loops in argumentation frameworks

Current approaches for giving semantics to abstract argumentation frameworks dismiss altogether any possibility of having conflicts among accepted arguments by requiring that the latter should be ‘conflict free’. In reality, however, contradictory phenomena coexist, or it may happen that one cannot make a choice between conflicting indications but still would like to keep track to all of them. For this purpose we introduce in this paper a new kind of argumentation semantics, called ‘conflict-tolerant’, in which all the accepted arguments must be justified (in the sense that each one of them can be defended), but some of them may still attack each other. In terms of graphical representation of argumentation systems, where attacks are represented by directed edges, this means that the possibility of accepting ‘loops’ of arguments is not automatically ruled out without any further considerations. To provide conflict-tolerant semantics we enhance the two standard approaches for defining coherent (conflict-free) semantics for argumentation frameworks. The extension-based approach is generalized by relaxing the ‘conflict-freeness’ requirement of the chosen sets of arguments, and the three-valued labeling approach is replaced by a four-valued labeling system that allows to capture mutual attacks among accepted arguments. We show that our setting is not a substitute of standard (conflict-free) semantics, but rather a generalized framework that accommodates both conflict-free and conflict-tolerant semantics. Moreover, the one-to-one relationship between extensions and labelings of conflict-free semantics is carried on to a similar correspondence between the extended approaches for providing conflict-tolerant semantics. Thus, in our setting as well, these are essentially two points of views for the same thing.

Minimal hypotheses: extension-based semantics to argumentation

The emptiness problem of the preferred semantics and the non-existence problem of the stable semantics are well recognized for argumentation frameworks. In this paper, we introduce two strong semantics, named s-preferred semantics and s-stable semantics, to guarantee the non-emptiness of the preferred extensions and the existence of the stable extensions respectively. Our semantics are defined by two concepts of extensions of argumentation frameworks, namely s-preferred extension and s-stable extension. Each is constructed in a similar way to the original semantics. The novelty of our semantics is that an extension of an argumentation framework is considered as a pair of sets of arguments, in which the second element of an extension is viewed as a kind of hypotheses that should be minimized. The s-preferred semantics not only solves the emptiness problem of the preferred semantics, but also coincides with the preferred semantics when nonempty preferred extensions exist. Meanwhile, the s-stable semantics ensures the existence of extensions, and coincides with the stable semantics when the stable extensions exist as well. The relations among various semantics for argumentation frameworks are discussed.