To better understand, and analyse, natural language arguments, it is desirable to represent them as logical arguments. However, most real-world arguments are enthymemes (i.e. some of the premises and/or claims are implicit), and therefore, there is a need to identify these implicit aspects. A ramification of this is that we may then need to edit some of the explicit premises and/or claim to remove redundant aspects and/or to allow the newly identified implicit formulae to work correctly with the explicit formulae. Furthermore, we may need to edit the claim so that it correctly attacks or supports other arguments as predicted by argument mining or as required by the user. To address these requirements, we propose a logic-based framework, based on classical propositional logic, for representing enthymemes, and manipulating them through a range of logical operations. We introduce meta-level rules to manipulate arguments (e.g. to add or delete premises, to edit claims, to split an argument into two arguments, and to merge two arguments into one). In order to direct the use of meta-level rules, we also introduce gain measures. When choosing a sequence of meta-level rules to apply, we can choose those that increase gain. This meta-level reasoning framework provides some clarity on the nature of enthymemes, and on how agents might elucidate them through a transparent and incremental process.

Gradual semantics for weighted bipolar argumentation provide a principled framework for modelling argumentative reasoning, yet existing approaches remain mostly scalar, fixed, and weakly grounded in empirical data. We introduce learnable multi-attribute gradual semantics for persuasion prediction in argumentative debates. Our approach builds a dataset of 600 textual debates converted into multi-attribute argumentation graphs enriched with multi-dimensional features on nodes and relations. Building on this representation, we propose learnable aggregation operators that distinguish intrinsic quality from persuasive strategy dimensions. Experiments show that the learned semantics achieve competitive performance with neural and LLM-based baselines while preserving interpretability.

This paper presents fast and exact methods for computing the probability of an argument’s acceptance using Dung’s semantics in the Constellation paradigm of Abstract Argumentation. For (directed) Singly-Connected Graphs (SCGs), the problem can now be solved in linearithmic time instead of being exponential in the number of attacks, as reported in the literature. Moreover, in the more general case of Directed Acyclic Graphs (DAGs), we provide an algorithm whose time complexity is linearithmic in the product of the out-degree of dependent arguments, i.e., arguments reaching the argument considered for acceptance through multiple paths in the graph. We theoretically show that this complexity is lower than the lower bound of the (exact) Constellation method, which is also supported by empirical results. Our approach to DAGs is also compared with the (approximate) Monte-Carlo method, which is stopped when exact results are obtained. Within this time constraint, Monte-Carlo still outputs significant errors, underlying the fast computation of our approach.

Argument mining is a natural language processing technology aimed at identifying the explicit premises and claims of arguments in text, and the support and attack relationships between them. To better understand, and automatically analyse, the argument maps that are output from argument mining, it would be desirable to instantiate the arguments in the argument map with logical arguments. However, most real-world arguments are enthymemes (i.e. some of the premises and/or claim are implicit), which need to be decoded (i.e. the implicit aspects need to be identified). A key challenge is to decode enthymemes so as to respect the support and attack relationships in the argument map. addressing the problem of identifying the missing premises and/or claim, and discerning the relationships between them. To address this, we present a novel framework, based on default logic, for representing arguments including enthymemes. We show how decoding an enthymeme means identifying the default rules that are implicit in the premises and claims. We then show how choosing a decoding of the enthymemes in an argument map can be formalized as an optimization problem, and that a solution can be obtained using MaxSAT solvers.

An argument can be seen as a pair of premises and a claim they support. Human arguments are often approximate, with some premises left implicit, leading to an implicit inference of the claim, i.e., forming enthymemes. To better understand and use them, we must decode these approximate enthymemes, typically by identifying missing premises to make the inference explicit, and, as we propose, by also removing irrelevant content to improve argument quality in specific contexts. Often, multiple decodings of an enthymeme are possible. However, no formal method has yet been proposed for identifying higher-quality decodings. To pave the way, we introduce six types of criteria for evaluating aspects of decodings. Then, we introduce the concept of a criterion measure, designed to evaluate decodings based on a specific criterion. In parallel, we define desirable properties for criterion measures, referred to as axioms, and we systematically evaluate our criterion measures with respect to them. Finally, we introduce the notion of quality measure that combine specific criterion measures to give an overall evaluation of the quality of decodings.

Abstract The study of Dung-style Argumentation Frameworks in recent years has focused on incorporating time. For example, availability intervals have been added to arguments and relations, resulting in different outputs of Dung semantics over time. This paper examines the probability distribution of arguments over time intervals. Using this temporal probabilistic model, the study explores how these frameworks can be transformed into a probabilistic argumentation according to the constellation approach and how they can be interpreted within the epistemic approach. The epistemic approach relies on the notion of defeat to select significant conflicts based on probability distributions. The study also introduces the temporal acceptability of arguments based on the concept of defence, allowing for more precise results over time. Finally, the models (constellation and epistemic) are extended to account for events that have a duration, i.e. that can occur for several consecutive instants of time.

Reasoning on inconsistent and uncertain data is challenging, especially for Knowledge-Graphs (KG) to abide temporal consistency. Our goal is to enhance inference with more general time interval semantics that specify their validity, as regularly found in historical sciences. We propose a new Temporal Markov Logic Networks (TMLN) model which extends the Markov Logic Networks (MLN) model with uncertain temporal facts and rules. Total and partial temporal (in)consistency relations between sets of temporal formulae are examined. We then propose a new Temporal Parametric Semantics (TPS) which allows combining several sub-functions leading to different assessment strategies. Finally, we present the new NeoMaPy tool, to compute the MAP inference on MLNs and TMLNs with several TPS. We compare our performances with state-of-the-art inference tools and exhibit faster and higher quality results.

Markov Logic Networks (MLN) are used for reasoning on uncertain and inconsistent temporal data. We proposed the TMLN (Temporal Markov Logic Network) which extends them with sorts/types, weights on rules and facts, and various temporal consistencies. The NeoMaPy framework integrates it as a knowledge graph based on conflict graphs which offers flexibility for reasoning with parametric Maximum A Posteriori (MAP) inferences, efficiency with an optimistic heuristic and interactive graph visualization for results explanation.

The paper discusses theoretical foundations that describe principles and processes involved in defining semantics that deal with similarity between arguments. Such semantics compute the strength of an argument on the basis of the strengths of its attackers, similarities between those attackers, and an initial weight ascribed to the argument. We define a semantics by three functions: an adjustment function that updates the strengths of attackers on the basis of their similarities, an aggregation function that computes the strength of the group of attackers, and an influence function that evaluates the impact of the group on the argument's initial weight. We propose intuitive constraints for the three functions and key rationality principles for semantics, and show how the former lead to the satisfaction of the latter. Then, we propose a broad family of semantics whose instances satisfy the principles. Finally, we analyse the existing adjustment functions and show that they violate some properties, then we propose novel ones and use them for generalizing h-Categorizer.

Ranking-based semantics are a way of assessing the acceptability of arguments in an abstract argumentation framework, by providing a ranking on arguments. This paper aims at going towards a generalization of the construction of such semantics, by investigating subsumption and incompatibility cases that may arise when principles that may enter into their composition are combined.