Argumentation is an important research area in the field of AI. There is a substantial amount of work on different aspects of Dung's abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are: i) extending the framework to account for recursive attacks and supports, and ii) considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects. We focus on High-Order Argumentation Frameworks with Necessities (HOAFNs) which allow for attack and support relations (interpreted as necessity) not only between arguments but also targeting attacks and supports at any level. We propose an approach for the incremental evaluation of the credulous acceptance problem in HOAFNs, by “incrementally” computing an extension (a set of accepted arguments, attacks and supports), if it exists, containing a given goal element in an updated HOAFN. In particular, we are interested in monitoring the credulous acceptance of a given argument, attack or support (goal) in an evolving HOAFN. Thus, our approach assumes to have a HOAFN Δ, a goal ϱ occurring in Δ, an extension E for Δ containing ϱ, and an update u establishing some changes in the original HOAFN, and uses the extension for first checking whether the update is relevant; for relevant updates, an extension of the updated HOAFN containing the goal is computed by translating the problem to the AF domain and leveraging on AF solvers. We provide formal results for our incremental approach and empirically show that it outperforms the evaluation from scratch of the credulous acceptance problem for an updated HOAFN.

Arguments in argumentation systems cannot always be considered as standalone entities, requiring the consideration of the pieces of evidence they rely on. This evidence might have to be retrieved from external sources such as databases or the web, and each attempt to retrieve a piece of evidence comes with an associated cost. Moreover, a piece of evidence may be available in a given scenario but not in others, and this is not known beforehand. As a result, the collection of active arguments (whose entire set of evidence is available) that can be used by the argumentation machinery of the system may vary from one scenario to another. In this work, we consider an Abstract Argumentation Framework with Fallible Evidence that accounts for these issues, and propose a heuristic measure used as part of the acceptability calculus (specifically, for building pruned dialectical trees) with the aim of minimizing the evidence retrieval cost of the arguments involved in the reasoning process. We provide an algorithmic solution that is empirically tested against two baselines and formally show the correctness of our approach.

An essential part of argumentation-based reasoning is to identify arguments in favor and against a statement or query, select the acceptable ones, and then determine whether or not the original statement should be accepted. We present here an abstract framework that considers two independent forms of argument interaction—support and conflict—and is able to represent distinctive information associated with these arguments. This information can enable additional actions such as: (i) a more in-depth analysis of the relations between the arguments; (ii) a representation of the user’s posture to help in focusing the argumentative process, optimizing the values of attributes associated with certain arguments; and (iii) an enhancement of the semantics taking advantage of the availability of richer information about argument acceptability. Thus, the classical semantic definitions are enhanced by analyzing a set of postulates they satisfy. Finally, a polynomial-time algorithm to perform the labeling process is introduced, in which the argument interactions are considered.

Argumentation is an important topic in the field of AI. There is a substantial amount of work about different aspects of Dung's abstract Argumentation Framework (AF). Two relevant aspects considered separately so far are extending the framework to account for recursive attacks and supports, and considering dynamics, i.e., AFs evolving over time. In this paper, we jointly deal with these two aspects. We focus on Attack-Support Argumentation Frameworks (ASAFs) which allow for attack and support relations not only between arguments but also targeting attacks and supports at any level, and propose an approach for the incremental computation of extensions (sets of accepted arguments, attacks and supports) of updated ASAFs. Our approach assumes that an initial ASAF extension is given and uses it for first checking whether updates are irrelevant; for relevant updates, an extension of an updated ASAF is computed by translating the problem to the AF domain and leveraging on AF solvers. We experimentally show our incremental approach outperforms the direct computation of extensions for updated ASAFs.

Abstract This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud’s rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then ’s DeLP notion of warrant and ASPIC+ ’s notion of justification are equivalent. This result is proven for three alternative definitions of attack.

The Attack-Support Argumentation Framework (ASAF) is an abstract argumentation framework that provides a unified setting for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. Currently, the extensions of the ASAF are obtained by translating it into a Dung's Argumentation Framework (AF). In this work we provide the ASAF with the ability of determining its extensions without requiring such a translation. We follow an extension-based approach for characterizing the acceptability semantics directly on the ASAF, considering the complete, preferred, stable and grounded semantics. Finally, we show that the proposed characterization satisfies different results from Dung's argumentation theory.

Inspired by the standard set theoretic Tarskian semantics, we propose a novel interpretation structure for studying the acceptability dynamics of arguments (i.e., the eventual changes on their acceptability condition) for logic-based argumentation. Interpretation structures identify possible scenarios in which a given argument would be accepted, or not, according to some standard extension-based argumentation semantics. These scenarios are configured in accordance to the consideration or inconsideration of other arguments from the given argumentation framework. Thereafter, it would be possible to ensure the acceptability of an argument by handling the evolution of the argumentation framework throughout the use of argumentative change operations. Hence, an interpretation structure which is a model of a given argument specifies a possible epistemic state to which the argumentation framework could evolve towards the argument's positive acceptability. Moreover, the analysis of several models of a given argument brings the opportunity of satisfying additional restrictions towards the evolution of a framework. Finally, we propose a revision operator whose rationality is ensured through postulates and a corresponding representation theorem.

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.

In this article, we extend Dung's formal approach from admissibility to less demanding extension semantics allowing arguments in cycles of attacks. We present an acceptance criterion leading to the characterization of three semantics called pairwise cogency , weak cogency and cyclic cogency . Particular game-theoretic protocols allow us to identify winning strategies with extensions in different semantics. Furthermore, an algorithmic characterization of those games exhibits clearly how self-attacking or in odd-length cycles of attack can be rationally managed beyond the limits of admissibility.

The problem of finding properties that characterizes the relation between argumentation semantics and argumentation inference operators has beginning to surface in the last years. Several works have addresses this concern proposing different “postulates” that reflect the intuitions in this respect. Argumentative reasoning is by nature defeasible and that distinct feature must have a deep influence on the resulting constrains. We believe that the very essence of argumentation should affect the manner in which the required properties are described.

Over the years, inconsistency management has caught the attention of researchers of different areas. Inconsistency is a problem that arises in many different scenarios, for instance, ontology development or knowledge integration. In such settings, it is important to have adequate automatic tools for handling conflicts that may appear in a knowledge base. We introduce an approach to consolidation of belief bases based on a refinement of kernel contraction that accounts for the relation among kernels using clusters instead. We define cluster contraction-based consolidation operators contraction by falsum on a belief base using cluster incision functions, a refinement of kernel incision functions.

The development of symbolic approaches to decision-making has become an ever-growing research line in artificial intelligence; argumentation has contributed to that with its unique strengths. Following this trend, this article proposes a general-purpose decision framework based on argumentation. Given a set of alternatives posed to the decision-maker, the framework represents the agent's preferences and knowledge by an epistemic component developed using possibilistic defeasible logic programming. The reasons by which a particular alternative is deemed better than another are explicitly considered in the argumentation process involved in warranting information from the epistemic component. The information warranted by the dialectical process is then used in decision rules that implement the agent's general decision-making policy. Essentially, decision rules establish patterns of behaviour of the agent specifying under which conditions a set of alternatives will be considered acceptable; moreover, a methodology for programming the agent's epistemic component is defined. It is demonstrated that programming the agent's epistemic component following this methodology exhibits some interesting properties with respect to the selected alternatives; also, when all the relevant information regarding the agent's preferences is specified, its choice behaviour coincides with respect to the optimum preference derived from a rational preference relation.

Abstract This article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to reason over potentially inconsistent de.l.p.s. Argument Theory Change (ATC) studies certain aspects of belief revision in order to make them suitable for abstract argumentation systems. In this article, abstract arguments are rendered concrete by using the particular rule-based defeasible logic adopted by DeLP. The objective of our proposal is to define prioritized argument revision operators à la ATC for de.l.p.s, in such a way that the newly inserted argument ends up undefeated after the revision, thus warranting its conclusion. In order to ensure this warrant, the de.l.p. has to be changed in concordance with a minimal change principle. To this end, we discuss different minimal change criteria that could be adopted. Finally, an algorithm is presented, implementing the argument revision operations.

In this work, we develop a game-theoretic framework in which pro and con arguments are put forward. This framework intends to capture winning strategies for different defense criteria. In turn, each possible extension semantics satisfies a particular defense criterion. To ensure that only semantics satisfying given criteria are obtained, protocols for playing have to be defined, being the ensuing winning strategies full characterizations of the corresponding criteria. Admissibility and strong admissibility are two of those criteria proposed in the literature for the evaluation of extension semantics; here, we also introduce two weaker criteria, pairwise and weak cogency, for the evaluation of non-admissible semantics, and we define specific game protocolscapturing them.

The significance of recommender systems has steadily grown in recent years as they help users to access relevant items from the vast universe of possibilities available these days. However, most of the research in recommenders is based purely on quantitative aspects, i.e., measures of similarity between items or users. In this paper we introduce a novel hybrid approach to refine recommendations achieved by quantitative methods with a qualitative approach based on argumentation, where suggestions are given after considering several arguments in favor or against the recommendations. In order to accomplish this, we use Defeasible Logic Programming (DeLP) as the underlying formalism for obtaining recommendations. This approach has a number of advantages over other existing recommendation techniques. In particular, recommendations can be refined at any time by adding new polished rules, and explanations may be provided supporting each recommendation in a way that can be easily understood by the user, by means of the computed arguments.

In this work we introduce an extension of an structured argumentation system in which presumptions are fully integrated in the reasoning mechanism. A presumption is defined as a piece of information that is tentatively taken to be true, usually in the absence of acceptable reasons to the contrary. In Presumptive Defeasible Logic Programming (PreDeLP), arguments can be built from both facts and presumptions. We analyze several criteria to compare arguments in PreDeLP, and highlight one possibility that captures the semantic difference between presumptions and facts or defeasible rules. On top of PreDeLP we develop a defeasible approach to argumentation-based diagnostic reasoning. The use of presumptions permits to extend the reasoning beyond factual information, creating in this way a universe of possible scenarios that support or interfere with a claim. We characterize the set of possible scenarios for and against a claim and identify those that best explain the warrant status of the query.

In abstract frameworks with varied strength attacks (AFV), arguments may attack each other with different strength. An admissible scenario is an admissible set of arguments fulfilling certain strength conditions about defences. In this work we analyze the computational complexity of some decision problems related to the quality of admissible scenarios: checking the property of being top-admissible and the property of being equilibrated. These problems are implying an exhaustive comparison between scenarios, and both of them are shown to be coNP-complete.

Argument Theory Change (ATC) applies classic belief change concepts to the area of argumentation. This intersection of fields takes advantage of the definition of a Dynamic Abstract Argumentation Framework, in which an argument is either active or inactive, and only in the former case it is taken into consideration in the reasoning process. ATC identifies how the framework has to be modified in order to achieve warrant for a certain argument. The present article copes with this matter by defining a revision operator based on activation of arguments, i.e., recognizing the knowledge that is missing.

This article introduces the notion of dynamics for abstract argumentation frameworks. We consider evidence as the basis from which arguments may be considered valid. The proposed Dynamic Argumentation Framework (DAF) is a refinement of Dung's abstract framework (AF), enriched with additional features. Since an instance of a DAF is equivalent to an AF, the former could be viewed as a template to build different AFs, applying the same knowledge to different situations. This equivalence is important, as we can take advantage of the vast amount of study on argumentation semantics for AFs to apply it to our approach. The DAF's aim is to provide a well-structured knowledge representation tool that allows for the definition of dynamics-aware argumentation-based systems.

In this work, we define Timed Abstract Argumentation Frameworks, a novel argumentation formalism where arguments are only valid for consideration in a given period of time, which is defined for every individual argument. Thus, the attainability of attacks and defenses is related to time, and the outcome of the framework may vary accordingly. We define a timed, interval-based notion of grounded extension as a skeptical semantics.

A computational grid is a distributed infrastructure that appears to the end user as one large computing resource across organization boundaries. Grid technologies enable large-scale sharing of resources within formal or informal consortia of individuals and/or institutions, usually called virtual organizations. In these settings, the discovery, characterization, management, and monitoring of resources, services, and computations can be challenging due to the considerable diversity, large numbers, dynamic behavior, and geographical distribution of the entities in which a user might be interested. Trust is one of the biggest concerns in the grid resource management field. Grid systems can employ reputation mechanisms in order to provide this essential trust, but not usually without incurring in certain additional costs that negate the potential performance gains offered by grid computing technologies. Moreover, current reputation mechanisms are not appropriate for resource management in large-scale systems. In this paper, we present a new reputation model for resource management based on a economy model. Also we demonstrate how it can by employed to add trust into algorithms for grid scheduling. Finally, we simulate the proposed resource management algorithm in order to verify its effectiveness.

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query $q$ will succeed when there is an argument ${\mathcal A}$ for $q$ that is warranted, i.e. the argument ${\mathcal A}$ that supports $q$ is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.