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)

RP-DeLP: a weighted defeasible argumentation framework based on a recursive semantics

In this paper we first define a recursive semantics for warranted formulas in a general defeasible argumentation framework by formalizing a notion of collective (non-binary) conflict among arguments. The recursive semantics for warranted formulas is based on the fact that if the argument is rejected, then all arguments built on it should also be rejected. The main characteristic of our recursive semantics is that an output (extension) of a knowledge base is a pair of sets of warranted and blocked formulas. Arguments for both warranted and blocked formulas are recursively based on warranted formulas but, while warranted formulas do not generate any collective conflict, blocked conclusions do. Formulas that are neither warranted nor blocked correspond to rejected formulas. Second we extend the general defeasible argumentation framework by attaching levels of preference to defeasible knowledge items and by providing a level-wise definition of warranted and blocked formulas. Third we formalize the warrant recursive semantics for the particular framework of Possibilistic Defeasible Logic Programming, we call this particular framework Recursive Possibilistic Defeasible Logic Programming (\mbox{RP-DeLP} for short), and we show its relevance in the scope of Political debates. An RP-DeLP program may have multiple outputs in case of circular definitions of conflicts among arguments. So, we tackle the problem of which output one should consider for an RP-DeLP program with multiple outputs. To this end we define the maximal ideal output of an RP-DeLP program as the set of conclusions which are ultimately warranted and we present an algorithm for computing them in polynomial space and with an upper bound on complexity equal to P^{NP}. Finally, we propose an efficient and scalable implementation of this algorithm that is based on implementing the two main queries of the system, looking for valid arguments and collective conflicts between arguments, using SAT encodings. We perform an experimental evaluation of our SAT based approach when solving test sets of instances with single and multiple preference levels for defeasible knowledge.The authors are very thankful to the anonymous reviewers for their helpful and constructive comments. This research was partially supported by the Spanish projects ARINF (TIN2009- 14704-C03-01), TASSAT (TIN2010-20967-C04-03), EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

Properties of ABA+ for Non-Monotonic Reasoning

We investigate properties of ABA+, a formalism that extends the well studied structured argumentation formalism Assumption-Based Argumentation (ABA) with a preference handling mechanism. In particular, we establish desirable properties that ABA+ semantics exhibit. These pave way to the satisfaction by ABA+ of some (arguably) desirable principles of preference handling in argumentation and nonmonotonic reasoning, as well as non-monotonic inference properties of ABA+ under various semantics.Comment: This is a revised version of the paper presented at the worksho

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

On the Implementation of a Multiple Output Algorithm for Defeasible Argumentation

In a previous work we defined a recursive warrant semantics for Defeasible Logic Programming based on a general notion of collective conflict among arguments. The main feature of this recursive semantics is that an output of a program is a pair consisting of a set of warranted and a set of blocked formulas. A program may have multiple outputs in case of circular definitions of conflicts among arguments. In this paper we design an algorithm for computing each output and we provide an experimental evaluation of the algorithm based on two SAT encodings defined for the two main combinatorial subproblems that arise when computing warranted and blocked conclusions for each output.The authors acknowledge the Spanish projects ARINF (TIN2009-14704-C03-01), TASSAT (TIN2010-20967-C04-03) and EdeTRI (TIN2012-39348-C02-01).Peer Reviewe