ABSTRACT. We extend the existing encoding of abstract argumentation frameworks in DL-PA (Dynamic Logic of Propositional Assignments) in order to capture different formalisms for arguing with qualitative forms of uncertainty. More in particular, we encode the main reasoning tasks of (rich) incomplete argumentation frameworks and control argumentation frameworks. After that, and inspired by our encoding, we define and study a new class of structures that are shown to be maximally expressive (called constrained incomplete argumentation frameworks).

ABSTRACT. We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

ABSTRACT. In this paper, we provide a formal framework to model the burden of persuasion in legal reasoning. The framework is based on abstract argumentation, a frequently studied method of non-monotonic reasoning, and can be applied to different argumentation semantics; it supports burdens of persuasion with arbitrary many levels, and allows for the placement of a burden of persuasion on any subset of an argumentation framework's arguments. Our framework can be considered an extension of related works that raise questions on how burdens of persuasion should be handled in some conflict scenarios that can be modeled with abstract argumentation. An open source software implementation of the introduced formal notions is available as an extension of an argumentation reasoning library.

ABSTRACT. In our paper [8], we have proposed a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks/supports whose targets are arguments or other attacks/supports) with an evidential meaning for supports, such frameworks are called REBAF. With this encoding, we are able to characterize the semantics of REBAF under the form of specific logical models. Nevertheless this encoding has two important drawbacks: first the handling of support cycles has some weaknesses and secondly the collective interactions (i.e. attacks or supports whose source is a set of arguments and not only one argument) are not taken into account. The current paper proposes an improvement of this encoding for solving these drawbacks.

[8] "Cayrol, C., Lagasquie-Schiex, M.C.: Logical encoding of argumentation frameworks with higher-order attacks and evidential supports (REBAF). International Journal on Artificial Intelligence Tools 29(3-4), 2060003:1–2060003:50 (June 2020). https://doi.org/10.1142/s0218213020600039".

ABSTRACT. Incomplete 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 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 AFs (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, that paves the way to the development of SAT-based solvers for reasoning with our new semantics for IAFs.

ABSTRACT. Dialogue systems are widely used in AI to support timely and interactive communication with users. We propose a general-purpose dialogue system architecture that leverages computational argumentation and state-of-the-art language technologies. We illustrate and evaluate the system using a COVID-19 vaccine information case study.

ABSTRACT. In this paper, we introduce a formal framework for the principle-based explanation of change of inference in abstract argumentation, in particular in the context of iterative inferences from a sequence of normal expansions, with a focus on admissible set-based semantics. The results allow us to provide, given an initial argumentation framework and an extension that has been inferred from it, principle-based explanations for the violation of monotony when inferring an extension from a normal expansion of the initial argumentation framework.

ABSTRACT. Abstract argumentation provides us with methods such as gradual and Dung semantics with which to evaluate arguments after potential attacks by other arguments. Some of these methods can take intrinsic strengths of arguments as input, with which to modulate the effects of attacks between arguments. Coming from abstract argumentation, these methods look only at the relations between arguments and not at the structure of the arguments themselves. In structured argumentation the way an argument is constructed, by chaining inference rules starting from premises, is taken into consideration. In this paper we study methods for assigning an argument its intrinsic strength, based on the strengths of the premises and inference rules used to form said argument. We first define a set of principles, which are properties that strength assigning methods might satisfy. We then propose two such methods and analyse which principles they satisfy. Finally, we present a generalised system for creating novel strength assigning methods and speak to the properties of this system regarding the proposed principles.

ABSTRACT. This paper presents a novel abstract argumentation framework, called Multi-Attack Argumentation Framework (MAAF), which supports different types of attacks. The introduction of types gives rise to a new family of non-standard semantics which can support applications that classical approaches cannot, while also allowing classical semantics as a special case. The main novelty of the proposed semantics is the discrimination among two different roles that attacks play, namely an attack as a generator of conflicts, and an attack as a means to defend an argument. These two roles have traditionally been considered together in the argumentation literature. Allowing some attack types to serve one of those roles only, gives rise to the different semantics presented here.