Formalisation and logical properties of the maximal ideal recursive semantics for weighted defeasible logic programming

Possibilistic defeasible logic programming (P-DeLP) is a logic programming framework which combines features from argumentation theory and logic programming, in which defeasible rules are attached with weights expressing their relative belief or preference strength. In P-DeLP,a conclusion succeeds if there exists an argument that entails the conclusion and this argument is found to be undefeated by a warrant procedure that systematically explores the universe of arguments in order to present an exhaustive synthesis of the relevant chains of pros and cons for the given conclusion. Recently, we have proposed a new warrant recursive semantics for P-DeLP, called Recursive P-DeLP (RP-DeLP for short), based on the claim that the acceptance of an argument should imply also the acceptance of all its sub-arguments which reflect the different premises on which the argument is based. This paper explores the relationship between the exhaustive dialectical analysis-based semantics of P-DeLP and the recursive-based semantics of RP-DeLP, and analyses a non-monotonic inference operator for RP-DeLP which models the expansion of a given program by adding new weighted facts associated with warranted conclusions. Given the recursive-based semantics of RP-DeLP, we have also implemented an argumentation framework for RP-DeLP that is able to compute not only the output of warranted and blocked conclusions, but also explain the reasons behind the status of each conclusion. We have developed this framework as a stand-alone application with a simple text-based input/output interface to be able to use it as part of other artificial intelligence systemsThis research was partially supported by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

Exploiting Parallelism for Hard Problems in Abstract Argumentation

Abstract argumentation framework (AF) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and enumeration problems associated to AF s are missing, thus potentially limiting the efficacy of argumentation-based approaches in real domains. In this paper, we present an algorithm for enumerating the preferred extensions of abstract argumentation frameworks which exploits parallel computation. To this purpose, the SCC-recursive semantics definition schema is adopted, where extensions are defined at the level of specific sub-frameworks. The algorithm shows significant performance improvements in large frameworks, in terms of number of solutions found and speedup

Multi-Context Reasoning in Continuous Data-Flow Environments

The field of artificial intelligence, research on knowledge representation and reasoning has originated a large variety of formats, languages, and formalisms. Over the decades many different tools emerged to use these underlying concepts. Each one has been designed with some specific application in mind and are even used nowadays, where the internet is seen as a service to be sufficient for the age of Industry 4.0 and the Internet of Things. In that vision of a connected world, with these many different formalisms and systems, a formal way to uniformly exchange information, such as knowledge and belief is imperative. That alone is not enough, because even more systems get integrated into the online world and nowadays we are confronted with a huge amount of continuously flowing data. Therefore a solution is needed to both, allowing the integration of information and dynamic reaction to the data which is provided in such continuous data-flow environments. This work aims to present a unique and novel pair of formalisms to tackle these two important needs by proposing an abstract and general solution. We introduce and discuss reactive Multi-Context Systems (rMCS), which allow one to utilise different knowledge representation formalisms, so-called contexts which are represented as an abstract logic framework, and exchange their beliefs through bridge rules with other contexts. These multiple contexts need to mutually agree on a common set of beliefs, an equilibrium of belief sets. While different Multi-Context Systems already exist, they are only solving this agreement problem once and are neither considering external data streams, nor are they reasoning continuously over time. rMCS will do this by adding means of reacting to input streams and allowing the bridge rules to reason with this new information. In addition we propose two different kind of bridge rules, declarative ones to find a mutual agreement and operational ones for adapting the current knowledge for future computations. The second framework is more abstract and allows computations to happen in an asynchronous way. These asynchronous Multi-Context Systems are aimed at modelling and describing communication between contexts, with different levels of self-management and centralised management of communication and computation. In this thesis rMCS will be analysed with respect to usability, consistency management, and computational complexity, while we will show how asynchronous Multi-Context Systems can be used to capture the asynchronous ideas and how to model an rMCS with it. Finally we will show how rMCSs are positioned in the current world of stream reasoning and that it can capture currently used technologies and therefore allows one to seamlessly connect different systems of these kinds with each other. Further on this also shows that rMCSs are expressive enough to simulate the mechanics used by these systems to compute the corresponding results on its own as an alternative to already existing ones. For asynchronous Multi-Context Systems, we will discuss how to use them and that they are a very versatile tool to describe communication and asynchronous computation

On the existence and multiplicity of extensions in dialectical argumentation

In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of extensions in terms of the notion of dialectical justification, a close cousin of the notion of admissibility. The characterization is given in the context of the particular logic for dialectical argumentation DEFLOG. The results are of direct relevance for several well-established models of defeasible reasoning (like default logic, logic programming and argumentation frameworks), since elsewhere dialectical argumentation has been shown to have close formal connections with these models.Comment: 10 pages; 9th International Workshop on Non-Monotonic Reasoning (NMR'2002

Computing Argumentation with Matrices

Abstract argumentation frameworks with finitely many arguments can be presented in matrix form. For this reason, the strengths and weaknesses of matrix operations are migrated from a mathematical representation to a computer science interpretation. We present matrix operation algorithms that can answer whether a given set of arguments is part of an argumentation extension

Joint attacks and accrual in argumentation frameworks

While modelling arguments, it is often useful to represent joint attacks, i.e., cases where multiple arguments jointly attack another (note that this is different from the case where multiple arguments attack another in isolation). Based on this remark, the notion of joint attacks has been proposed as a useful extension of classical Abstract Argumentation Frameworks, and has been shown to constitute a genuine extension in terms of expressive power. In this chapter, we review various works considering the notion of joint attacks from various perspectives, including abstract and structured frameworks. Moreover, we present results detailing the relation among frameworks with joint attacks and classical argumentation frameworks, computational aspects, and applications of joint attacks. Last but not least, we propose a roadmap for future research on the subject, identifying gaps in current research and important research directions.Fil: Bikakis, Antonis. University College London; Estados UnidosFil: Cohen, Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Dvoák, Wolfgang. Technische Universitat Wien; AustriaFil: Flouris, Giorgos. Foundation for Research and Technology; GreciaFil: Parsons, Simon. University of Lincoln; Reino Unid

A generalised framework for dispute derivations in assumption-based argumentation

AbstractAssumption-based argumentation is a general-purpose argumentation framework with well-understood theoretical foundations and viable computational mechanisms (in the form of dispute derivations), as well as several applications. However, the existing computational mechanisms have several limitations, hindering their deployment in practice: (i) they are defined in terms of implicit parameters, that nonetheless need to be instantiated at implementation time; (ii) they are variations (for computing different semantics) of one another, but still require different implementation efforts; (iii) they reduce the problem of computing arguments to the problem of computing assumptions supporting these arguments, even though applications of argumentation require a justification of claims in terms of explicit arguments and attacks between them.In this context, the contribution of this paper is two-fold. Firstly, we provide a unified view of the existing (GB-, AB- and IB-)dispute derivations (for computation under the grounded, admissible and ideal semantics, respectively), by obtaining them as special instances of a single notion of X-dispute derivations that, in addition, renders explicit the implicit parameters in the original dispute derivations. Thus, X-dispute derivations address issues (i) and (ii). Secondly, we define structured X-dispute derivations, extending X-dispute derivations by computing explicitly the underlying arguments and attacks, in addition to assumptions. Thus, structured X-dispute derivations also address issue (iii). We prove soundness and completeness results for appropriate instances of (structured) X-dispute derivations, w.r.t. the grounded, admissible and ideal semantics, thus laying the necessary theoretical foundations for deployability thereof