The rule $\mathrm{Defeated}(x) \leftarrow \mathrm{Attacks}(y,x),\, \neg \, \mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF). An argument $x$ is defeated ($\mathrm{OUT}$) if there exists an undefeated argument $y$ that attacks it. For 2-valued (stable) solutions, this is the case iff $y$ is accepted ($\mathrm{IN}$), i.e., if all of $y$'s attackers are defeated. Under WFS, arguments that are neither accepted nor defeated are undecided ($\mathrm{UNDEC}$). As shown in prior work, well-founded solutions (a.k.a. grounded labelings) "explain themselves": The provenance of arguments is given by subgraphs (definable via regular path queries) rooted at the node of interest. This provenance is closely related to winning strategies of a two-player argumentation game. We present a novel approach for extending this provenance to stable AF solutions. Unlike grounded solutions, which can be constructed via a bottom-up alternating fixpoint procedure, stable models often involve non-deterministic choice as part of the search for models. Thus, the provenance of stable solutions is of a different nature, and reflects a more expressive generate & test paradigm. Our approach identifies minimal sets of critical attacks, pinpointing choices and assumptions made by a stable model. These critical attack edges provide additional insights into the provenance of an argument's status, combining well-founded derivation steps with choice steps. Our approach can be understood as a form of diagnosis that finds minimal "repairs" to an AF graph such that the well-founded solution of the repaired graph coincides with the desired stable model of the original AF graph.
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings, constructing a choice function via a relation on the alternatives is not always possible. However, we show that one can always construct a choice function via a linear order on sets of alternatives, even when a fallback value is encoded as the minimal element in the linear order. The axiomatics of such choice functions are presented for the general case and the case of union-closed input restrictions. Restricted choice structures have applications in knowledge representation and reasoning, and here we discuss their applications for theory change and abstract argumentation.
We introduce Gradual Abstract Argumentation for Case-Based Reasoning (Gradual AA-CBR), a data-driven, neurosymbolic classification model in which the outcome is determined by an argumentation debate structure that is learned simultaneously with neural-based feature extractors. Each argument in the debate is an observed case from the training data, favouring their labelling. Cases attack or support those with opposing or agreeing labellings, with the strength of each argument and relationship learned through gradient-based methods. This argumentation debate structure provides human-aligned reasoning, improving model interpretability compared to traditional neural networks (NNs). Unlike the existing purely symbolic variant, Abstract Argumentation for Case-Based Reasoning (AA-CBR), Gradual AA-CBR is capable of multi-class classification, automatic learning of feature and data point importance, assigning uncertainty values to outcomes, using all available data points, and does not require binary features. We show that Gradual AA-CBR performs comparably to NNs whilst significantly outperforming existing AA-CBR formulations.
Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between them, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulous or skeptical acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision, counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend the significance of specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.
Monitoring and analyzing process traces is a critical task for modern companies and organizations. In scenarios where there is a gap between trace events and reference business activities, this entails an interpretation problem, amounting to translating each event of any ongoing trace into the corresponding step of the activity instance. Building on a recent approach that frames the interpretation problem as an acceptance problem within an Abstract Argumentation Framework (AAF), one can elegantly analyze plausible event interpretations (possibly in an aggregated form), as well as offer explanations for those that conflict with prior process knowledge. Since, in settings where event-to-activity mapping is highly uncertain (or simply under-specified) this reasoning-based approach may yield lowly-informative results and heavy computation, one can think of discovering a sequencetagging model, trained to suggest highly-probable candidate event interpretations in a context-aware way. However, training such a model optimally may require using a large amount of manually-annotated example traces. Considering the urgent need of developing Green AI solutions enabling environmental and societal sustainability (with reduced labor/computational costs and carbon footprint), we propose a data/computation-efficient neuro-symbolic approach to the problem, where the candidate interpretations returned by the example-driven sequence tagger is refined by the AAF-based reasoner. This allows us to also leverage prior knowledge to compensate for the scarcity of example data, as confirmed by experimental results; clearly, this property is particularly useful in settings where data annotation and model optimization costs are subject to stringent constraints.
Datalog$^\neg$ is a central formalism used in a variety of domains ranging from deductive databases and abstract argumentation frameworks to answer set programming. Its model theory is the finite counterpart of the logical semantics developed for normal logic programs, mainly based on the notions of Clark's completion and two-valued or three-valued canonical models including supported, stable, regular and well-founded models. In this paper we establish a formal link between Datalog$^\neg$ and Boolean network theory first introduced for gene regulatory networks. We show that in the absence of odd cycles in a Datalog$^\neg$ program, the regular models coincide with the stable models, which entails the existence of stable models, and in the absence of even cycles, we prove the uniqueness of stable partial models and regular models. This connection also gives new upper bounds on the numbers of stable partial, regular, and stable models of a Datalog$^\neg$ program using the cardinality of a feedback vertex set in its atom dependency graph. Interestingly, our connection to Boolean network theory also points us to the notion of trap spaces. In particular we show the equivalence between subset-minimal stable trap spaces and regular models.
In cooperative human decision-making, agreements are often not total; a partial degree of agreement is sufficient to commit to a decision and move on, as long as one is somewhat confident that the involved parties are likely to stand by their commitment in the future, given no drastic unexpected changes. In this paper, we introduce the notion of agreement scenarios that allow artificial autonomous agents to reach such agreements, using formal models of argumentation, in particular abstract argumentation and value-based argumentation. We introduce the notions of degrees of satisfaction and (minimum, mean, and median) agreement, as well as a measure of the impact a value in a value-based argumentation framework has on these notions. We then analyze how degrees of agreement are affected when agreement scenarios are expanded with new information, to shed light on the reliability of partial agreements in dynamic scenarios. An implementation of the introduced concepts is provided as part of an argumentation-based reasoning software library.
In recent years, large language models (LLMs) have made significant advancements in neuro-symbolic computing. However, the combination of LLM with argumentation computation remains an underexplored domain, despite its considerable potential for real-world applications requiring defeasible reasoning. In this paper, we aim to investigate the capability of LLMs in determining the extensions of various abstract argumentation semantics. To achieve this, we develop and curate a benchmark comprising diverse abstract argumentation frameworks, accompanied by detailed explanations of algorithms for computing extensions. Subsequently, we fine-tune LLMs on the proposed benchmark, focusing on two fundamental extension-solving tasks. As a comparative baseline, LLMs are evaluated using a chain-of-thought approach, where they struggle to accurately compute semantics. In the experiments, we demonstrate that the process explanation plays a crucial role in semantics computation learning. Models trained with explanations show superior generalization accuracy compared to those trained solely with question-answer pairs. Furthermore, by leveraging the self-explanation capabilities of LLMs, our approach provides detailed illustrations that mitigate the lack of transparency typically associated with neural networks. Our findings contribute to the broader understanding of LLMs' potential in argumentation computation, offering promising avenues for further research in this domain.
In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property.
Provenance in databases has been thoroughly studied for positive and for recursive queries, then for first-order (FO) queries, i.e., having negation but no recursion. Query evaluation can be understood as a two-player game where the opponents argue whether or not a tuple is in the query answer. This game-theoretic approach yields a natural provenance model for FO queries, unifying how and why-not provenance. Here, we study the fine-grain structure of game provenance. A game $G=(V,E)$ consists of positions $V$ and moves $E$ and can be solved by computing the well-founded model of a single, unstratifiable rule: \[ \text{win}(X) \leftarrow \text{move}(X, Y), \neg \, \text{win}(Y). \] In the solved game $G^{\lambda}$, the value of a position $x\,{\in}\,V$ is either won, lost, or drawn. This value is explained by the provenance $\mathscr{P}$(x), i.e., certain (annotated) edges reachable from $x$. We identify seven edge types that give rise to new kinds of provenance, i.e., potential, actual, and primary, and demonstrate that "not all moves are created equal". We describe the new provenance types, show how they can be computed while solving games, and discuss applications, e.g., for abstract argumentation frameworks.
An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome of this dialogue. In this paper, we propose a new framework for modelling abstract argumentation graphs, a model that incorporates the order of enunciation of arguments. By taking this order into account, we have the means to deduce a unique outcome for each dialogue, called an extension. We also establish several properties, such as termination and correctness, and discuss two notions of completeness. In particular, we propose a modification of the previous transformation based on a "last enunciated last updated" strategy, which verifies the second form of completeness.
In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic function over binary variables (0/1), where the coefficients can be represented by a symmetric square matrix (or an equivalent upper triangular version). With the QUBO formulation, exploiting new computing architectures, such as Quantum and Digital Annealers, is possible. A more conventional approach consists of developing approximate solvers, which, in this case, are used to tackle the intrinsic complexity. We performed tests to prove the correctness and applicability of classical problems in Argumentation and enforcement of argument sets. We compared our approach to two other approximate solvers in the literature during tests. In the final experimentation, we used a Simulated Annealing algorithm on a local machine. Also, we tested a Quantum Annealer from the D-Wave Ocean SDK and the Leap Quantum Cloud Service.
We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions that have no non-empty {\tau}-extension in their reduct (vacuity condition). We give a systematic overview on vacuous reduct semantics resulting from combining different admissibility-based and conflict-free semantics and present a principle-based analysis of vacuous reduct semantics in general. We provide criteria for the inheritance of principle satisfaction by a vacuous reduct semantics from its base and vacuity condition for established as well as recently introduced principles in the context of weak argumentation semantics. We also conduct a principle-based analysis for the special case of undisputed semantics.
Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.
Dung's Abstract Argumentation Framework (AF) has emerged as a key formalism for argumentation in Artificial Intelligence. It has been extended in several directions, including the possibility to express supports, leading to the development of the Bipolar Argumentation Framework (BAF), and recursive attacks and supports, resulting in the Recursive BAF (Rec-BAF). Different interpretations of supports have been proposed, whereas for Rec-BAF (where the target of attacks and supports may also be attacks and supports) even different semantics for attacks have been defined. However, the semantics of these frameworks have either not been defined in the presence of support cycles, or are often quite intricate in terms of the involved definitions. We encompass this limitation and present classical semantics for general BAF and Rec-BAF and show that the semantics for specific BAF and Rec-BAF frameworks can be defined by very simple and intuitive modifications of that defined for the case of AF. This is achieved by providing a modular definition of the sets of defeated and acceptable elements for each AF-based framework. We also characterize, in an elegant and uniform way, the semantics of general BAF and Rec-BAF in terms of logic programming and partial stable model semantics.
In the pursuit of enhancing the efficacy and flexibility of interpretable, data-driven classification models, this work introduces a novel incorporation of user-defined preferences with Abstract Argumentation and Case-Based Reasoning (CBR). Specifically, we introduce Preference-Based Abstract Argumentation for Case-Based Reasoning (which we call AA-CBR-P), allowing users to define multiple approaches to compare cases with an ordering that specifies their preference over these comparison approaches. We prove that the model inherently follows these preferences when making predictions and show that previous abstract argumentation for case-based reasoning approaches are insufficient at expressing preferences over constituents of an argument. We then demonstrate how this can be applied to a real-world medical dataset sourced from a clinical trial evaluating differing assessment methods of patients with a primary brain tumour. We show empirically that our approach outperforms other interpretable machine learning models on this dataset.
A framework with sets of attacking arguments (SETAF) is an extension of the well-known Dung's Abstract Argumentation Frameworks (AAFs) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic Programs (NLPs) to SETAFs and vice versa, from SETAFs to NLPs. We show that there is pairwise equivalence between their semantics, including the equivalence between L-stable and semi-stable semantics. Furthermore, for a class of NLPs called Redundancy-Free Atomic Logic Programs (RFALPs), there is also a structural equivalence as these back-and-forth translations are each other's inverse. Then, we show that RFALPs are as expressive as NLPs by transforming any NLP into an equivalent RFALP through a series of program transformations already known in the literature. We also show that these program transformations are confluent, meaning that every NLP will be transformed into a unique RFALP. The results presented in this paper enhance our understanding that NLPs and SETAFs are essentially the same formalism. Under consideration in Theory and Practice of Logic Programming (TPLP).
Explainable Artificial Intelligence and Formal Argumentation have received significant attention in recent years. Argumentation-based systems often lack explainability while supporting decision-making processes. Counterfactual and semifactual explanations are interpretability techniques that provide insights into the outcome of a model by generating alternative hypothetical instances. While there has been important work on counterfactual and semifactual explanations for Machine Learning models, less attention has been devoted to these kinds of problems in argumentation. In this paper, we explore counterfactual and semifactual reasoning in abstract Argumentation Framework. We investigate the computational complexity of counterfactual- and semifactual-based reasoning problems, showing that they are generally harder than classical argumentation problems such as credulous and skeptical acceptance. Finally, we show that counterfactual and semifactual queries can be encoded in weak-constrained Argumentation Framework, and provide a computational strategy through ASP solvers.
Various approaches have been proposed for providing efficient computational approaches for abstract argumentation. Among them, neural networks have permitted to solve various decision problems, notably related to arguments (credulous or skeptical) acceptability. In this work, we push further this study in various ways. First, relying on the state-of-the-art approach AFGCN, we show how we can improve the performances of the Graph Convolutional Networks (GCNs) regarding both runtime and accuracy. Then, we show that it is possible to improve even more the efficiency of the approach by modifying the architecture of the network, using Graph Attention Networks (GATs) instead.
We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from an argumentation framework, there is a lack of justification behind their acceptability based on implicit argument preferences. Preference-based argumentation frameworks allow one to determine what arguments are justified given a set of preferences. Our research considers the inverse of the standard reasoning problem, i.e., given an abstract argumentation framework and a set of justified arguments, we compute what the possible preferences over arguments are. Furthermore, there is a need to verify (i.e., assess) that the computed preferences would lead to the acceptable sets of arguments. This paper presents a novel approach and algorithm for exhaustively computing and enumerating all possible sets of preferences (restricted to three identified cases) for a conflict-free set of arguments in an abstract argumentation framework. We prove the soundness, completeness and termination of the algorithm. The research establishes that preferences are determined using an extension-based approach after the evaluation phase (acceptability of arguments) rather than stated beforehand. In this work, we focus our research study on grounded, preferred and stable semantics. We show that the complexity of computing sets of preferences is exponential in the number of arguments, and thus, describe an approximate approach and algorithm to compute the preferences. Furthermore, we present novel algorithms for verifying (i.e., assessing) the computed preferences. We provide details of the implementation of the algorithms (source code has been made available), various experiments performed to evaluate the algorithms and the analysis of the results.