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.

We extend belief revision theory from propositional logic to the modal logic S5. Our first contribution takes the form of three new postulates (M1-M3) that go beyond the AGM ones and capture the idea of minimal change in the presence of modalities. Concerning the construction of modal revision operations, we work with set pseudo-distances, i.e., distances between sets of points that may violate the triangle-inequality. Our second contribution is the identification of three axioms (A3-A5) that go beyond the standard axioms of metrics. Loosely speaking, our main result states the following: if a pseudo-distance satisfies certain axioms, then the induced revision operation satisfies (M1-M3). We investigate three pseudo-distances from the literature (Dhaus, Dinj, Dsum), and the three induced revision operations (*Haus, *Inj, *Sum). Using our main result, we show that only *Sum satisfies (M1-M3) all together. As a last contribution, we revisit a major criticism of AGM operations, namely that the revisions of (p ∧ q) and (p ∧ (p → q)) are identical. We show that the problem disappears if instead of material implication we use the modal operator of strict implication that can be defined in S5.

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.

Improving trust in decisions made by classification models is becoming crucial for the acceptance of automated systems, and an important way of doing that is by providing explanations for the behaviour of the models. Different explainers have been proposed in the recent literature for that purpose, however their formal properties are under-studied. This paper investigates theoretically explainers that provide reasons behind decisions independently of instances. Its contributions are fourfold. The first is to lay the foundations of such explainers by proposing key axioms, i.e., desirable properties they would satisfy. Two axioms are incompatible leading to two subsets. The second contribution consists of demonstrating that the first subset of axioms characterizes a family of explainers that return sufficient reasons while the second characterizes a family that provides necessary reasons. This sheds light on the axioms which distinguish the two types of reasons. As a third contribution, the paper introduces various explainers of both families, and fully characterizes some of them. Those explainers make use of the whole feature space. The fourth contribution is a family of explainers that generate explanations from finite datasets (subsets of the feature space). This family, seen as an abstraction of Anchors and LIME, violates some axioms including one which prevents incorrect explanations.

The paper studies how arguments can be evaluated in weighted bipolar argumentation graphs (i.e., graphs whose arguments have basic weights and may be supported and attacked). It introduces principles that an evaluation method (or semantics) would satisfy, analyzes existing semantics with respect to them, and finally proposes a new semantics for the class of non-maximal acyclic graphs.

The paper studies semantics that evaluate arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

In an argumentation setting, a semantics evaluates the overall acceptability of arguments. Consequently, it reveals the global loss incurred by each argument due to attacks. However, it does not say anything on the contribution of each attack to that loss. This paper introduces the novel concept of contribution measure which evaluates those contributions. It starts by defining a set of axioms that a reasonable measure would satisfy, then shows that the Shapley value is the unique measure that satisfies them. Finally, it investigates the properties of the latter under existing semantics.

The theory of preferential consequence relations has been investigated extensively in the classical context, where copies of classical valuations serve as the terms of the preference relation. The first purpose of the present paper is to extend the theory to preferential consequence relations in certain three/four-valued contexts, well-known as the paraconsistent logics J3 and FOUR. We give characterizations of several families of preferential consequence relations in these two contexts. Our second and main purpose is to investigate a qualified version of preferential consequence, which we call preferential-discriminative consequence. This is defined to hold between a set Γ of formulae and formula α iff Γ ⊢ α but Γ ⊬ ¬ α where ⊢ is the plain relation. We provide characterizations of several families of such preferential-discriminative consequence relations for all of the classical, three, and four-valued contexts.

A pivotal consequence relation is defined to hold between a set of formulas Γ and formula α iff every non-negligible model for Γ is a model for α. Unlike preferential consequence relations, the set of all non-negligible (or preferred) valuations is fixed and thus does not depend on the premisses under consideration. The first purpose of the present paper is to investigate pivotal consequence relations. We provide characterizations of several families in the classical framework, but also in certain three/four-valued frameworks, well-known as the paraconsistent logics J3 and ℱ𝒪𝒰ℛ. We show also that there is no ‘normal’ characterization of the family of all pivotal consequence relations, in the infinite classical framework. And we show a link with X-logics. Our second purpose is to investigate a qualified version of pivotal consequence, which we call pivotal-discriminative consequence. This is defined to hold between a set of formulas Γ and formula α iff Γ ⊢ α but Γ ⊬ ¬α, where ⊢ is the plain relation. We provide characterizations of several families of such relations for the classical, three, and four-valued frameworks.