Francesc Guitart

Using Answer Set Programming for an Scalable Implementation of Defeasible Argumentation

In previous works, a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules was introduced. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. In this paper we propose an efficient and scalable implementation of an interpreter for RP-DeLP using Answer Set Programming (ASP) encodings for the two main queries of the system: looking for valid arguments and finding collective conflicts among arguments. We perform an experimental evaluation of our ASP approach and we compare the results with a previously proposed SAT based approach. The results show that with ASP we are able to scale up to bigger problem instances.

Maximal ideal recursive semantics for defeasible argumentation

In a previous work we defined a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. An output of an RP-DeLP program is a pair of sets of warranted and blocked conclusions (literals), all of them recursively based on warranted conclusions but, while warranted conclusions do not generate any conflict, blocked conclusions do. An RP-DeLP program may have multiple outputs in case of circular definitions of conflicts among arguments. In this paper 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 RPDeLP 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 PNP.

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.

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 systems.

On the Characterization of the Maximal Ideal Recursive Semantics of RP-DeLP.

This research was partially supported by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER- INGENIO 2010, CSD2007-00022)

Web Based System for Weighted Defeasible Argumentation

In a previous work we defined a recursive semantics for reasoning about which arguments should be warranted when extending Defeasible Argumentation with defeasibility levels for arguments. Our approach is based on a general notion of collective conflict among arguments and on the fact that if an argument is warranted it must be that all its sub-arguments also are warranted. An output of a program is a pair consisting of a set of warranted and a set of blocked arguments with maximum strength. Arguments that are neither warranted nor blocked correspond to rejected arguments. On this recursive semantics a program may have multiple outputs in case of circular definitions of conflicts among arguments and for these circular definitions of conflicts we define what output, called maximal ideal output, should be considered based on the claim that if an argument is excluded from an output, then all the arguments built on top of it should also be excluded from that output. In this paper we show a web based system we have designed and implemented to compute the output for programs with single and multiple outputs. For programs with multiple outputs the system also computes the maximal ideal output. An interesting feature of the system is that it provides not only both sets of warranted an blocked arguments with maximum strength but also useful information that allows to better understand why an argument is either warranted, blocked or rejected.