From Structured to Abstract Argumentation : Assumption-Based Acceptance via AF Reasoning

Peer reviewe

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)

Declarative Algorithms and Complexity Results for Assumption-Based Argumentation

Peer reviewe

On the equivalence between assumption-based argumentation and logic programming

Assumption-Based Argumentation (ABA) has been shown to subsume various other non-monotonic reasoning formalisms, among them normal logic programming (LP). We re-examine the relationship between ABA and LP and show that normal LP also subsumes (flat) ABA. More precisely, we specify a procedure that given a (flat) ABA framework yields an associated logic program with almost the same syntax whose semantics coincide with those of the ABA framework. That is, the 3-valued stable (respectively well-founded, regular, 2-valued stable, and ideal) models of the associated logic program coincide with the complete (respectively grounded, preferred, stable, and ideal) assumption labellings and extensions of the ABA framework. Moreover, we show how our results on the translation from ABA to LP can be reapplied for a reverse translation from LP to ABA, and observe that some of the existing results in the literature are in fact special cases of our work. Overall, we show that (flat) ABA frameworks can be seen as normal logic programs with a slightly different syntax. This implies that methods developed for one of these formalisms can be equivalently applied to the other by simply modifying the syntax

Assumption-based Argumentation Dialogues

Formal argumentation based dialogue models have attracted some research interests recently. Within this line of research, we propose a formal model for argumentation-based dialogues between agents, using assumption-based argumentation (ABA). Thus, the dialogues amount to conducting an argumentation process in ABA. The model is given in terms of ABA-specific utterances, debate trees and forests implicitly built during and drawn from dialogues, legal-move functions (amounting to protocols) and outcome functions. Moreover, we investigate the strategic behaviour of agents in dialogues, using strategy-move functions. We instantiate our dialogue model in a range of dialogue types studied in the literature, including information-seeking, inquiry, persuasion, conflict resolution, and discovery. Finally, we prove (1) a formal connection between dialogues and well-known argumentation semantics, and (2) soundness and completeness results for our dialogue models and dialogue strategies used in different dialogue types

Algorithms for argument systems

Argument systems are computational models that enable an artificial intelligent agent to reason via argumentation. Basically, the computations in argument systems can be viewed as search problems. In general, for a wide range of such problems existing algorithms lack five important features. Firstly, there is no comprehensive study that shows which algorithm among existing others is the most efficient in solving a particular problem. Secondly, there is no work that establishes the use of cost-effective heuristics leading to more efficient algorithms. Thirdly, mechanisms for pruning the search space are understudied, and hence, further pruning techniques might be neglected. Fourthly, diverse decision problems, for extended models of argument systems, are left without dedicated algorithms fine-tuned to the specific requirements of the respective extended model. Fifthly, some existing algorithms are presented in a high level that leaves some aspects of the computations unspecified, and therefore, implementations are rendered open to different interpretations. The work presented in this thesis tries to address all these concerns. Concisely, the presented work is centered around a widely studied view of what computationally defines an argument system. According to this view, an argument system is a pair: a set of abstract arguments and a binary relation that captures the conflicting arguments. Then, to resolve an instance of argument systems the acceptable arguments must be decided according to a set of criteria that collectively define the argumentation semantics. For different motivations there are various argumentation semantics. Equally, several proposals in the literature present extended models that stretch the basic two components of an argument system usually by incorporating more elements and/or broadening the nature of the existing components. This work designs algorithms that solve decision problems in the basic form of argument systems as well as in some other extended models. Likewise, new algorithms are developed that deal with different argumentation semantics. We evaluate our algorithms against existing algorithms experimentally where sufficient indications highlight that the new algorithms are superior with respect to their running time

Algorithms for computational argumentation in artificial intelligence

Argumentation is a vital aspect of intelligent behaviour by humans. It provides the means for comparing information by analysing pros and cons when trying to make a decision. Formalising argumentation in computational environment has become a topic of increasing interest in artificial intelligence research over the last decade. Computational argumentation involves reasoning with uncertainty by making use of logic in order to formalize the presentation of arguments and counterarguments and deal with conflicting information. A common assumption for logic-based argumentation is that an argument is a pair where Φ is a consistent set which is minimal for entailing a claim α. Different logics provide different definitions for consistency and entailment and hence give different options for formalising arguments and counterarguments. The expressivity of classical propositional logic allows for complicated knowledge to be represented but its computational cost is an issue. This thesis is based on monological argumentation using classical propositional logic [12] and aims in developing algorithms that are viable despite the computational cost. The proposed solution adapts well established techniques for automated theorem proving, based on resolution and connection graphs. A connection graph is a graph where each node is a clause and each arc denotes there exist complementary disjuncts between nodes. A connection graph allows for a substantially reduced search space to be used when seeking all the arguments for a claim from a given knowledgebase. In addition, its structure provides information on how its nodes can be linked with each other by resolution, providing this way the basis for applying algorithms which search for arguments by traversing the graph. The correctness of this approach is supported by theoretical results, while experimental evaluation demonstrates the viability of the algorithms developed. In addition, an extension of the theoretical work for propositional logic to first-order logic is introduced

Negotiating Socially Optimal Allocations of Resources with Argumentation

The resource allocation problem of multi-agent systems is the problem of deciding how to allocate resources, controlled by agents, to agents within a given system. Agents typically have preferences over alternative allocations of resources. These preferences may be derived from the agents’ goals, which can be fulfilled by different plans (sets of resources). The problem arises because agents may not be able to fulfil their goals without being re-allocated resources controlled by other agents and agents may have conflicting preferences over allocations. Examples of the resource allocation problem include electronic commerce (where resources are commodities equipped with prices), the grid (where resources are computational entities equipped with computational power), and scheduling and timetabling (where resources may be tasks with costs). The focus in this thesis is distributed decision-making amongst agents, whereby agents actively participate in computing re-allocations, starting from initial allocations which may or may not fulfil their goals. A re-allocation is arrived at by means of local negotiation steps wherein resources change hands between the agents involved in the negotiations. The negotiation method of choice in this thesis is argumentation-based negotiation supported by assumption-based argumentation. This method allows agents to work towards their goals despite incomplete information regarding the goals of and resources allocated to other agents, to share knowledge, thereby eliminating unknowns, and to resolve conflicts within themselves and between one another which may arise because of inconsistent information. Solutions generated by a resource allocation mechanism may be ranked according to how they affect the individual welfare of the agents as well as the overall social welfare of the agent society, according to different notions of social welfare borrowed from economics. The argumentation-based negotiation mechanism we propose guarantees, for the problem domain of interest in this thesis, that negotiations between agents always terminate converging to a solution. Moreover, the mechanism guarantees that solutions reached optimise the welfare of the individual agents as well as the agent society as a whole according to Pareto optimal and utilitarian notions of social welfare