Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision operation should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those distinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a (...) dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors. (shrink)

This paper addresses the issue of the dynamic enforcement of a constraint in an argumentation system. The system consists in (1) an argumentation framework, made up, notably, of a set of arguments...

dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes wit...

This paper studies a fundamental mechanism by which conflicts between arguments are drawn from sentiments regarding acceptability of the arguments. Given sets of arguments, an inverse abstract argumentation problem seeks attack relations between arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in each of the attack relations. It is an inverse problem of the traditional problem we refer to as the forward abstract argumentation problem. Given an attack relation, the forward abstract argumentation (...) problem seeks sets of arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in the attack relation. We give a probabilistic model of argumentation-theoretic inference. It is a generative model formalising the process by which acceptability semantics interprets acceptability of arguments in a given attack relation. We show that it gives a broad view of solutions to the forward and inverse abstract argumentation problems. Specifically, solutions to the inverse and forward abstract argumentation problems are shown to be equivalent to a maximum likelihood estimate and maximum likelihood prediction, respectively, which are both available with the generative model. In addition, they are shown to be special cases of the posterior distribution and the evidence, respectively, which are both obtained by probabilistic inference on the generative model. We report an experiment result and application example of the generative model in the inverse problems. (shrink)

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are (...) interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable. (shrink)

Cases or examples can be often explained by the interplay of arguments in favour or against their outcomes. This paper addresses the problem of finding explanations for a collection of cases where an explanation is a labelled argumentation graph consistent with the cases, and a case is represented as a statement labelling. The focus is on semi-abstract argumentation graphs specifying attack and subargument relations between arguments, along with particular complete argument labellings taken from probabilistic argumentation where arguments can be excluded. (...) The framework and computational considerations lead to an iterated local iterative deepening depth-first search to collect ‘interesting’ semi-abstract argumentation graphs consistent with a collection of statement labellings. Finally, the framework is illustrated and evaluated with a proof-of-concept implementation. (shrink)

In the current paper we re-examine the concepts of attack semantics and collective attacks in abstract argumentation, and examine how these concepts interact with each other. For this, we systematically map the space of possibilities. Starting with standard argumentation frameworks (which consist of a directed graph with nodes and arrows) we briefly state both node semantics and arrow semantics (the latter a.k.a. attack semantics) in both their extensions-based form and labellings-based form. We then proceed with SETAFs (which consist of a (...) directed hypergraph of nodes and arrows, to take into account the notion of collective attacks) and state both node semantics and arrow semantics, in both their extensions-based and labellings-based form. We then show equivalence between the extensions-based and labellings-based form, for node semantics and arrow semantics of AFs, as well as for node semantics and arrow semantics of SETAFs. Moreover, we show equivalence between node semantics and arrow semantics for AFs, and equivalence between node semantics and arrow semantics for SETAFs (with the notable exception of semi-stable). We also provide a novel way of converting a SETAF to an AF such that semantics are preserved, without the use of any “meta arguments”. Although the main part of our work is on the level of abstract argumentation, we do provide an application of our theory on the instantiated level. More specifically, we show that the classical characterisation of Assumption-Based Argumentation (ABA) can be seen as an instantiation based on a SETAF, whereas the contemporary characterisation of ABA can be seen as an instantiation based on a standard AF. Our theory of how to convert a SETAF to an AF can then be used to account for both the similarities and the differences between the classical and contemporary characterisations of ABA. Most prominently, our theory is able to explain the semantic mismatch for semi-stable semantics that arises in the ABA instantiation process. (shrink)