Assumption-based Argumentation Frameworks Research Articles

Non-flat ABA Is an Instance of Bipolar Argumentation

Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism, whereby arguments and attacks between them are drawn from rules, defeasible assumptions and their contraries. A common restriction imposed on ABA frameworks (ABAFs) is that they are flat, i.e. each of the defeasible assumptions can only be assumed, but not derived. While it is known that flat ABAFs can be translated into abstract argumentation frameworks (AFs) as proposed by Dung, no translation exists from general, possibly non-flat ABAFs into any kind of abstract argumentation formalism. In this paper, we close this gap and show that bipolar AFs (BAFs) can instantiate general ABAFs. To this end we develop suitable, novel BAF semantics which borrow from the notion of deductive support. We investigate basic properties of our BAFs, including computational complexity, and prove the desired relation to ABAFs under several semantics.

Redefining ABA+ Semantics via Abstract Set-to-Set Attacks

Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing qualitative comparison between assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics---grounded and complete semantics---is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture ABA+. Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA+ and HYPAFs to obtain variants for grounded and complete ABA+ semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA+ semantics.

On Dynamics in Structured Argumentation Formalisms

This paper is a contribution to the research on dynamics in assumption-based argumentation (ABA). We investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Notably, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semanticspreserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the abstract framework. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture dynamics in ABA. This yields the desired tractable fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

Justifying convolutional neural network with argumentation for explainability

Convolutional neural network (CNN) has emerged as one of the most accurate methods for sentiment analysis, but it is largely uninterpretable, while case-based reasoning (CBR) is less accurate but o ff ers interpretable outputs in the form of arguments from analogy. This paper presents an approach to combine these two methods, CNN for accuracy and CBR for explainability, using an assumption-based argumentation (ABA) framework. Our approach focuses on justifying CNN outputs using analogous sentences from CBR, while ensuring that the combined process is argumentative and hence self-explainable. To demonstrate the proposal, we construct a CNN model M 1 and a CBR model M 2 for sentiment analysis using di ff erent subsets of a dataset of which the remaining part is used for testing and comparing these input models with combined models. For an input sentence, if M 1 and M 2 predict the same sentiment, then the analogous sentence, which M 2 finds, is used to explain the sentiment. If they give conflicting sentiments, a hybrid model M 3 determines which one should be followed using a system of strict rules that takes into account how assertive M 1 and M 2 are. Another hybrid model M 4 , which is implemented by an ABA framework, improves on M 3 by considering the probability distribution of the set of all labels from M 1 , and the second (or third) most similar sentences from M 2 . M 3 and M 4 preserve the accuracy of the CNN model (specifically, 88.32% and 88.28% in comparison with 87.59% accuracy of the CNN). They justify 69.95% and 74.53% of CNN outputs, respectively.

Simple contrapositive assumption-based argumentation part II: Reasoning with preferences

Simple contrapositive assumption-based argumentation frameworks are a general setting for structured argumentation, providing a robust approach to reasoning with arguments and counter-arguments. In this paper we extend these frameworks with priorities and introduce some new results concerning the Dung's semantics of the resulting formalisms.

Declarative Algorithms and Complexity Results for Assumption-Based Argumentation

The study of computational models for argumentation is a vibrant area of artificial intelligence and, in particular, knowledge representation and reasoning research. Arguments most often have an intrinsic structure made explicit through derivations from more basic structures. Computational models for structured argumentation enable making the internal structure of arguments explicit. Assumption-based argumentation (ABA) is a central structured formalism for argumentation in AI. In this article, we make both algorithmic and complexity-theoretic advances in the study of ABA. In terms of algorithms, we propose a new approach to reasoning in a commonly studied fragment of ABA (namely the logic programming fragment) with and without preferences. While previous approaches to reasoning over ABA frameworks apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct declarative approach to ABA reasoning by encoding ABA reasoning tasks in answer set programming. We show via an extensive empirical evaluation that our approach significantly improves on the empirical performance of current ABA reasoning systems. In terms of computational complexity, while the complexity of reasoning over ABA frameworks is well-understood, the complexity of reasoning in the ABA+ formalism integrating preferences into ABA is currently not fully established. Towards bridging this gap, our results suggest that the integration of preferential information into ABA via so-called reverse attacks results in increased problem complexity for several central argumentation semantics.

Simple contrapositive assumption-based argumentation frameworks

Assumption-based argumentation is one of the most prominent formalisms for logical (or structured) argumentation, with tight links to different forms of defeasible reasoning. In this paper we study the Dung semantics for extended forms of assumption-based argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible assumptions are expressed by arbitrary formulas in that logic. We show that unless the falsity propositional constant is part of the defeasible assumptions, the grounded and the well-founded semantics for ABFs lack most of the desirable properties they have in abstract argumentation frameworks (AAFs), and that for simple definitions of the contrariness operator and the attacks relations, preferred and stable semantics are reduced to naive semantics. We also show the redundancy of the closure condition in the standard definition of Dung's semantics for ABFs, and investigate the use of disjunctive attacks in this setting. Finally, we show some close relations of reasoning with ABFs to reasoning with maximally consistent sets of premises, and consider some properties of the induced entailments, such as being cumulative, preferential, or rational relations that satisfy non-interference.

On Construction and Evaluation of Analogical Arguments for Persuasive Reasoning

ABSTRACTAnalogical reasoning is a complex process based on a comparison between two pairs of concepts or states of affairs (aka. the source and the target) for characterizing certain features from one to another. Arguments which employ this process to support their claims are called analogical arguments. Our goals are to study the structure and the computation for their defeasibility in light of the argumentation theory. Our proposed assumption-based argumentation with predicate similarity ABA(p) framework can be seen as an extension of assumption-based argumentation framework (ABA), in which not only assumptions can be used but also similarity of predicates is used to support a claim. ABA (p) labels each argument tree with an analogical degree and different ways to aggregate numerical values are studied toward gullible/skeptical characteristics in agent reasoning. The acceptability of analogical arguments is evaluated w.r.t. the semantics of abstract argumentation. Finally, we demonstrate that ABA (p) captures the argumentation scheme for argument from analogy and provides an explanation when it is used for persuasion.

On the Equivalence between Assumption-Based Argumentation and Logic Programming

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.

Labellings for assumption-based and abstract argumentation

The semantics of Assumption-Based Argumentation (ABA) frameworks are traditionally characterised as assumption extensions, i.e. sets of accepted assumptions. Assumption labellings are an alternative way to express the semantics of flat ABA frameworks, where one of the labels in, out, or undec is assigned to each assumption. They are beneficial for applications where it is important to distinguish not only between accepted and non-accepted assumptions, but further divide the non-accepted assumptions into those which are clearly rejected and those which are neither accepted nor rejected and thus undecided. We prove one-to-one correspondences between assumption labellings and extensions for the admissible, grounded, complete, preferred, ideal, semi-stable and stable semantics. We also show how the definition of assumption labellings for flat ABA frameworks can be extended to assumption labellings for any (flat and non-flat) ABA framework, enabling reasoning with a wider range of scenarios. Since flat ABA frameworks are structured instances of Abstract Argumentation (AA) frameworks, we furthermore investigate the relation between assumption labellings for flat ABA frameworks and argument labellings for AA frameworks. Building upon prior work on complete assumption and argument labellings, we prove one-to-one correspondences between grounded, preferred, ideal, and stable assumption and argument labellings, and a one-to-many correspondence between admissible assumption and argument labellings. Inspired by the notion of admissible assumption labellings we introduce committed admissible argument labellings for AA frameworks, which correspond more closely to admissible assumption labellings of ABA frameworks than admissible argument labellings do.

Argument graphs and assumption-based argumentation

Arguments in structured argumentation are usually defined as trees, and extensions as sets of such tree-based arguments with various properties depending on the particular argumentation semantics. However, these arguments and extensions may have redundancies as well as circularities, which are conceptually and computationally undesirable. Focusing on the specific case of Assumption-Based Argumentation (ABA), we propose novel notions of arguments and admissible/grounded extensions, both defined in terms of graphs. We show that this avoids the redundancies and circularities of standard accounts, and set out the relationship to standard tree-based arguments and admissible/grounded extensions (as sets of arguments). We also define new notions of graph-based admissible/grounded dispute derivations for ABA, for determining whether specific sentences hold under the admissible/grounded semantics. We show that these new derivations are superior with respect to standard dispute derivations in that they are complete in general, rather than solely for restricted classes of ABA frameworks. Finally, we present several experiments comparing the implementation of graph-based admissible/grounded dispute derivations with implementations of standard dispute derivations, suggesting that the graph-based approach is computationally advantageous.

Graphical Representation of Assumption-Based Argumentation

Since Assumption-Based Argumentation (ABA) was introduced in the nineties,the structure and semantics of an ABA framework have been studied exclusively in logical termswithout any graphical representation.Here, we show how an ABA framework and its complete semantics can be displayed in a graph,clarifying the structure of the ABA framework as well as the resulting complete assumption labellings.Furthermore, we show that such an ABA graph can be used to represent the structureand semantics of a logic program (LP), based on the correspondence between the semantics of a LP and an ABA framework encoding this LP.

The computational complexity of ideal semantics

We analyse the computational complexity of the recently proposed ideal semantics within both abstract argumentation frameworks ( afs) and assumption-based argumentation frameworks ( abfs). It is shown that while typically less tractable than credulous admissibi-lity semantics, the natural decision problems arising with this extension-based model can, perhaps surprisingly, be decided more efficiently than sceptical preferred semantics. In particular the task of finding the unique ideal extension is easier than that of deciding if a given argument is accepted under the sceptical semantics. We provide efficient algorithmic approaches for the class of bipartite argumentation frameworks and, finally, present a number of technical results which offer strong indications that typical problems in ideal argumentation are complete for the class p ∥ C of languages decidable by polynomial time algorithms allowed to make non-adaptive queries to a C oracle, where C is an upper bound on the computational complexity of deciding credulous acceptance: C = np for afs and logic programming ( lp) instantiations of abfs; C = Σ 2 p for abfs modelling default theories.

Computing ideal sceptical argumentation

We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114–159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114–159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114–159] that is sound for the sceptical grounded semantics.