Mauro Javier Gómez Lucero

Modelling Argument Accrual in Possibilistic Defeasible Logic Programming

Argumentation frameworks have proven to be a successful approach to formalizing commonsense reasoning. Recently, some argumentation frameworks have been extended to deal with possibilistic uncertainty, notably Possibilistic Defeasible Logic Programming (P-DeLP). At the same time, modelling argument accrual has gained attention from the argumentation community. Even though some preliminary formalizations have been advanced, they do not take into account possibilistic uncertainty when accruing arguments. In this paper we present a novel approach to model argument accrual in the context of P-DeLP in a constructive way.

Modelling argument accrual with possibilistic uncertainty in a logic programming setting

Argumentation frameworks have proven to be a successful approach to formalizing commonsense reasoning. Recently, some argumentation frameworks have emerged which incorporate the treatment of possibilistic uncertainty, notably Possibilistic Defeasible Logic Programming (P-DeLP). At the same time, modelling argument accrual has gained attention from the argumentation community. Even though some preliminary formalizations have been advanced, they do not take into account possibilistic uncertainty when accruing arguments. In this paper we present a novel approach to model argument accrual with possibilistic uncertainty in a constructive way. The formalization proposed uses P-DeLPs representation language and notion of argument as a basis.

An approach to argumentation considering attacks through time

In the last decade, several argument-based formalisms have emerged, with application in many areas, such as legal reasoning, autonomous agents and multi-agent systems; many are based on Dungs seminal work characterizing Abstract Argumentation Frameworks (AF). Recent research in the area has led to Temporal Argumentation Frameworks (TAF), that extend AF by considering the temporal availability of arguments. A new framework was introduced in subsequent research, called Extended Temporal Argumentation Framework (E-TAF), extending TAF with the capability of modeling the availability of attacks among arguments. E-TAF is powerful enough to model different time-dependent properties associated with arguments; moreover, we will present an instantiation of the abstract framework E-TAF on an extension of Defeasible Logic Programming (DeLP) incorporating the representation of temporal availability and strength factors of arguments varying over time, associating these characteristics with the language of DeLP. The strength factors are used to model different more concrete measures such as reliability, priorities, etc.; the information is propagated to the level of arguments, then the E-TAF definitions are applied establishing their temporal acceptability.

Modeling time and valuation in structured argumentation frameworks

Temporal Argumentation Frameworks (TAF) represent a recent extension of Dungs abstract argumentation frameworks that consider the temporal availability of arguments. In a TAF, arguments are valid during specific time intervals, called availability intervals, while the attack relation of the framework remains static and permanent in time; thus, in general, when identifying the set of acceptable arguments, the outcome associated with a TAF will vary in time. We introduce an extension of TAF, called Extended Temporal Argumentation Framework (E-TAF), adding the capability of modeling the temporal availability of attacks among arguments, thus modeling special features of arguments varying over time and the possibility that attacks are only available in a given time interval.E-TAF will be enriched by considering Structured Abstract Argumentation, using Dynamic Argumentation Frameworks. The resulting framework, E - TAF ? , provides a suitable model for different time-dependent issues satisfying properties and equivalence results that permit to contrast the expressivity of E-TAF and E - TAF ? with argumentation based on abstract frameworks. Thus, the main contribution here is to provide an enhanced framework for modeling special features of argumentation varying over time, which are relevant in many real-world situations. The proposal aims at advancing in the integration of time and valuation in the context of argumentation systems as well.

A labeled argumentation framework

To increase the expressivity of an argumentation formalism, we propose adding meta-level information to the arguments in the form of labels representing quantifiable data such as reliability degree, strength measure, skill, time availability, or any other feature about arguments. The extra information attached to an argument is then used in the acceptability determination process.We present a Labeled Argumentation Framework (LAF), combining the knowledge representation capabilities provided by the Argument Interchange Format (AIF) with an Algebra of Argumentation Labels, enabling us to handle the labels associated with the arguments. These labels are propagated through an argumentative graph according to the relations of support, conflict, and aggregation between arguments. Through this process we obtain final labels attached to the arguments that are useful to determine their acceptability.

An AIF-Based Labeled Argumentation Framework

Adding meta-level information to the arguments in the form of labels extends the representational capabilities of an argumentation formalism, expanding its capabilities. Labels allow the representation of different features: skill, reliability, strength, time availability, or any other that might be related to arguments; then, this information can be used to determine the strength of an argument and assist in the process of determining arguments acceptability. We have developed a framework called Labeled Argumentation Framework LAF based in the Argument Interchange Format AIF, integrating the handling of labels; thus, labels associated with arguments will be combined and propagated according to argument interactions, such as support, conflict, and aggregation. Through this process, we will establish argument acceptability, where the final labels propagated to the acceptable arguments provide additional acceptability information, such as degree of justification, or explanation, among others.

Formalization of argument accrual: Acceptability semantics and dialectical proof procedure

Argumentation is a powerful paradigm able to formalize commonsense reasoning, finding application in different domains such as automated reasoning, decision making, legal dispute, automated negotiation, etc. However, most of these argumentation-based formalizations do not model the notion of argument accrual, which has been recently gaining importance. This thesis defines a novel formalization of argument accrual, including a declarative characterization of this notion and an associated operational characterization addressing computation. The proposed formalization makes contributions to the existing accrual approaches, mainly concerning the answers obtained, answer explanation, accrual evaluation and comparison, and efficiency of computation.