Reasoning in Structured Argumentation: Assumption-based Argumentation and ASPIC+

Abstract

Research in computational argumentation, as a branch in Arti cial Intelligence (AI), is dedicated to study representations of arguments and to develop automated argumentative reasoning. The sub eld of structured argumentation comprises of several approaches, which describe how to perform rational and automated argumentative reasoning, usually based on rule-based knowledge bases. From such bases arguments, and relations among arguments, are instantiated. Subsequently, reasoning can be carried out on the constructed arguments, oftentimes without the need to consider the internal structure of these arguments. In this way, argumentation semantics drive the reasoning process on such abstracted arguments. In recent years, research on computational aspects, i.e., developing theoretical foundations, algorithmic approaches, and systems, for structured argumentation has gained signi cant traction in the research community. We give an overview of recent strands of research on two prominent structured argumentation formalisms: assumption-based argumentation (ABA) and ASPIC+. We look at issues and bene ts arising from instantiation or explication of arguments, discuss complexity results and algorithms for reasoning in ABA and ASPIC+, and consider how incorporation of preferences changes the picture. We close with open issues and possible directions for future research.

Keywords

• eol>Computational argumentation
• computational complexity
• algorithms

Knowledge base

b! a? c!

Instantiate

arguments a b

c d e

Evaluate

acceptability a b

c d e

Draw conclusions

b and e

We focus in this talk on recent advances in algorithmic approaches to two prominent forms of structured argumentation: assumption-based argumentation (ABA) [ 4, 18 ] and ASPIC+ [ 5 ]. In brief, algorithms operate either by explication (instantiation) of arguments and relations between arguments [ 19, 20 ] or by computation directly on the given knowledge base (rule base) [ 21, 22 ]. The latter approach does not construct any arguments and works by selection of “defeasible elements” in the given knowledge base (such as assumptions or defeasible rules) and checking whether these provide a “compact” representation of a set of acceptable arguments.

Explication of arguments has the advantage that reasoning can be carried out on (relatively) simple structures (abstract arguments and attacks in many cases) and such arguments can also be utilized for argumentative explanations of results. On the other hand, the number of arguments to be generated can be high, e.g., exponential in the general case [ 23, 19, 20 ]. Computationally speaking, reasoning after explication of arguments is usually NP (coNP) hard, i.e., still complex after a possibly expensive argument generation. Operating without arguments thus has the advantage to potentially avoid costly intermediate structures not strictly required for solving reasoning.

Current experimental results favour the non-explication route of algorithms [ 21, 22 ], yet not in all cases [ 19, 20 ], e.g., when the complexity of solving a task on the knowledge base is higher than solving the task on a generated AF, as then the (costly) argument generation may pay o , which is the case, e.g., when considering non- at ABA.

In this talk, we give an overview of such recent algorithmic and computational advances in the eld of structured argumentation, and also discuss impacts of preferential reasoning that oftentimes increases complexity of reasoning.

Acknowledgments This research was supported by the Austrian Science Fund (FWF) by grant P35632.

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