Declarative Algorithms and Complexity Results for Assumption-Based Argumentation

A key ingredient of computational argumentation in AI is the generation of arguments in favor of or against claims under scrutiny. In this paper we look at the complexity of argument construction and reasoning in the prominent structured formalism of assumption-based argumentation (ABA). We point out that reasoning in ABA by means of constructing an abstract argumentation framework (AF) gives rise to two main sources of complexity: (i) constructing the AF and (ii) reasoning within the constructed graph. Since both steps are intractable in general, it is no surprise that the best performing state-of-the-art ABA reasoners skip the instantiation procedure entirely and perform tasks directly on the input knowledge base. Driven by this observation, we identify and study atomic and symmetric ABA, two ABA fragments that preserve the expressive power of general ABA, and that can be utilized to have milder complexity in the first or second step. We show that using atomic ABA allows for an instantiation procedure for general ABA leading to polynomially-bounded AFs and that symmetric ABA can be used to create AFs that have mild complexity to reason on. By an experimental evaluation, we show that using the former approach with modern AF solvers can be competitive with state-of-the-art ABA solvers, improving on previous AF instantiation approaches that are hindered by intractable argument construction.

The existing approaches which map the given explicit preferences into standard assumption-based argumentation frameworks (ABAs) reveal some difficulties such as generating a huge number of rules and so on. To overcome them, we present an assumption-based argumentation framework equipped with preferences (p_ABA). It increases the expressive power of ABA by incorporating preferences between sentences into the framework. The semantics of p_ABAs is given by \(\mathcal{P}\) extensions selected from extensions of ABAs based on the given sentence ordering. The advantages of our approach are that not only it enables us to express different kinds of preferences such as preferences over rules, over goals, over decisions by means of sentence orderings in p_ABAs but we also successfully obtain solutions from \(\mathcal{P}\) extensions of the p_ABAs expressing the respective knowledge for various applications such as epistemic reasoning, practical reasoning, decision-making with preferences and so on in a uniform way without suffering from difficulties of existing ones.

Since Assumption-Based Argumentation (ABA) was introduced in the nineties,the structure and semantics of an ABA framework have been studied exclusively in logical termswithout any graphical representation.Here, we show how an ABA framework and its complete semantics can be displayed in a graph,clarifying the structure of the ABA framework as well as the resulting complete assumption labellings.Furthermore, we show that such an ABA graph can be used to represent the structureand semantics of a logic program (LP), based on the correspondence between the semantics of a LP and an ABA framework encoding this LP.

Assumption-based argumentation can serve as an effective computational tool for argumentation-based epistemic and practical reasoning, as required in a number of applications. In this paper we substantiate this claim by presenting formal mappings from frameworks for epistemic and practical reasoning onto assumption-based argumentation frameworks. We also correlate these mappings to formulations of epistemic and practical reasoning in abstract argumentation terms.KeywordsPractical ReasoningInference RuleLogic ProgrammingDeductive SystemStrict RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A major research direction in AI argumentation is the study and development of practical computational techniques for reasoning in different argumentation formalisms. Compared to abstract argumentation, developing algorithmic techniques for different structured argumentation formalisms, such as assumption-based argumentation and the general ASPIC+ framework, is more challenging. At present, there is a lack of efficient approaches to reasoning in ASPIC+. We develop a direct declarative approach based on answer set programming (ASP) to reasoning in an instantiation of the ASPIC+ framework. We establish formal foundations for direct declarative encodings for reasoning in ASPIC+ without preferences for several central argumentation semantics, and detail ASP encodings of semantics for which reasoning about acceptance is NP-hard in ASPIC+. Empirically, the ASP approach scales up to frameworks of significant size, thereby answering the current lack of practical computational approaches to reasoning in ASPIC+ and providing a promising base for capturing further generalizations within ASPIC+.

Computational argumentation is primed to strengthen the current hot research field of Explainable Artificial Intelligence (XAI), e.g., by dialectical approaches. In this paper, we extend and discuss a recently proposed approach of so-called strong acceptance on abstract argumentation that aims to support explaining argumentative acceptance. Our goal is to push these results into the realm of structured argumentation. In this setting, a knowledge base induces an abstract argumentation framework (AF) via instantiation. We investigate how and under which conditions it is possible to transfer results regarding strong acceptance between the given knowledge base and the induced AF. To this end we consider generic functions formalizing the interaction of the AF and the knowledge base. This approach helps us to infer rather general results making basic assumptions rather than dealing with the technical details of several structured argumentation formalisms. Along the way, we apply our techniques to the concrete approach of assumption-based argumentation (ABA) which constitutes one of the primal structured argumentation formalisms.

In the twenty years since the creation of the stable model semantics[4] for logic programs and inclusion of both classical and negation as failure, answer set programming (ASP)[1] has grown from a small fledgeling field within logic programming to a maturing field of its own. In this extended abstract we discuss some future application areas for ASP and theoretic and implementational problems that need to be addressed in order to make them feasible. With the increase in efficiency of the answer set solvers and a better understanding of the formalism, its advantages and disadvantages, more applications areas for ASP are found. While traditional application domains were mainly in the knowledge representation and reasoning area, we now also see more and more applications in areas were competitors like SAT or CSP were considered better alternatives. We believe, these current applications are just the tip of the iceberg. In years to come, we will see more and more successful applications plus further expansion and improvements on existing applications. In recent years we have seen a lot of ASP activity in the fields of the semantic web and web-services with specific workshops dedicated to the topic1. We believe that these fields hold more potential for years to come. For example, ASP could also be used for match-making and service coordination and orchestration. Another application area of ASP is multi-agent systems. In most cases this was always on the more theoretical side of applications. To our knowledge, nobody has used ASP to construct a running multi-agent system where the agents use ASP for reasoning purposes. With our current solvers, we should be able to provide such a system. ASP has also be applied in wide variety of other domains like planning, diagnosis, language-evolution, policy-design, bio-informatics, compiler optimisation, music composition, security, cryptography and game design. Most of these application are in a prototype phase, demonstrating that ASP could be of value in this domain and are slowly making their way to conferences and journals in the domain they are addressing. By doing some domain experts will get to know ASP and its capabilities. In time this will lead to them pointing ASP researchers to similar problems in the same domain. So in the medium term, we believe we can look forward to more ASP applications in bio-informatics, e-health, medicine, e-government and engineering. Normally we refer to ASP as a problem solving paradigm. We model the problem as an ASP program such that the answer sets correspond to the solutions of this problem.

Conflicts exist in multi-agent systems for a number of reasons: agents have different interests and desires; agents hold different beliefs; agents make different assumptions. To resolve conflicts, agents need to better convey information to each other and facilitate fair negotiations yielding jointly agreeable outcomes. We present a two-agent, dialogical conflict resolution scheme developed with the Assumption-Based Argumentation (ABA) framework.

We introduce a novel method to aggregate Bipolar Argumentation (BA) Frameworks expressing opinions by different parties in debates. We use Bipolar Assumption-based Argumentation (ABA) as an all-encompassing formalism for BA under different semantics. By leveraging on recent results on judgement aggregation in Social Choice Theory, we prove several preservation results, both positive and negative, for relevant properties of Bipolar ABA.

Argumentation has gained traction as a formalism to make more transparent decisions and provide formal explanations recently. In this paper, we present an argumentation-based approach to decision making that can support modelling and automated reasoning about complex qualitative preferences and offer dialogical explanations for the decisions made. We first propose Qualitative Preference Decision Frameworks (QPDFs). In a QPDF, we use contextual priority to represent the relative importance of combinations of goals in different contexts and define associated strategies for deriving decision preferences based on prioritized goal combinations. To automate the decision computation, we map QPDFs to Assumption-based Argumentation (ABA) frameworks so that we can utilize existing ABA argumentative engines for our implementation. We implemented our approach for two tasks, diagnostics and prognostics of Alzheimer's Disease (AD), and evaluated it with real-world datasets. For each task, one of our models achieves the highest accuracy and good precision and recall for all classes compared to common machine learning models. Moreover, we study how to formalize argumentation dialogues that give contrastive, focused and selected explanations for the most preferred decisions selected in given contexts.

We present a prototypical system, plasp, implementing Planning by compilation to Answer Set Programming (ASP). Our approach is inspired by Planning as Satisfiability, yet it aims at keeping the actual compilation simple in favor of modeling planning techniques by meta-programming in ASP. This has several advantages. First, ASP modelings are easily modifiable and can be studied in a transparent setting. Second, we can take advantage of available ASP grounders to obtain propositional representations. Third, we can harness ASP solvers providing incremental solving mechanisms. Finally, the ASP community gains access to a wide range of planning problems, and the planning community benefits from the knowledge representation and reasoning capacities of ASP.KeywordsPlanning ProblemOperator SplittingConcurrent ActionPropositional RepresentationAutomate PlanningThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We give some design guidelines for argumentation systems. These guidelines are meant to indicate essential features of argumentation when used to support “practical reasoning”. We express the guidelines in terms of postulates. We use a notion of redundancy to provide a formal counterpart of these postulates. We study the satisfaction of these postulates in two existing argumentation frameworks: assumption-based argumentation and argumentation in classical logic.

Home networks are a fast growing market but managing them is a difficult task, and diagnosing faults is even more challenging. Current fault management tools provide comprehensive information about the network and the devices but it is left to the user to interpret and reason about the data and experiment in order to find the cause of a problem. Home users may not have motivation or time to learn the required skills. Furthermore current tools adopt a closed approach which hardcodes a knowledge base, making them hard to update and extend. This paper proposes an open fault management framework for home networks, whose goal is to simplify network troubleshooting for non-expert users. The framework is based on assumption-based argumentation that is an AI technique for knowledge representation and reasoning. With the underlying argumentation theory, we can easily capture and model the diagnosis procedures of network administrators. The framework is rule-based and extensible, allowing new rules to be added into the knowledge base and diagnostic strategies to be updated on the fly.The framework can also utilise external knowledge and make distributed diagnosis.

Answer Set Programming (ASP) has emerged in the recent years as a powerful paradigm for declarative problem solving, which has its roots in knowledge representation and non-monotonic logic programming. Similar to SAT solving, the basic idea is to encode solutions to a problem in the models of a non-monotonic logic program, which can be computed by reasoning engines off the shelf. ASP is particularly well-suited for modeling and solving problems which involve common sense reasoning or transitive closure, and has been fruitfully applied to a growing range of applications. Among the latter are also problems in testing and verfication, for which efficient core fragments of ASP that embrace Datalog haven been exploited. This talk gives a brief introduction to ASP, covering the basic concepts, some of its properties and features, and solvers. It further addresses some applications in the context of verification and recent developments in ASP, which bring evaluation closer to other formalisms and logics.

Answer Set Programming (ASP) is a rule-based language rooted in traditional Logic Programming, Databases, Knowledge Representation, and Nonmonotonic Reasoning. It offers a flexible language for declarative problem solving, with support of efficient general-purpose solvers and reasoners. The larger part of this article provides an introduction to ASP, with a historical perspective, a definition of the core language, a guideline to knowledge representation, and an overview of existing ASP solvers. One part focuses on one commonly used feature: aggregates and generalized atoms. The inclusion of aggregates in ASP (and Logic Programming at large) has long been motivated, however there are some issues with semantics to be addressed, in particular when aggregates occur in recursive definitions. Very similar considerations are needed when coupling ASP with other formalisms, which we collectively refer to as “generalized atoms”. An overview of these semantic challenges and proposals for addressing them is provided, along with an overview of complexity results and system support.