Encoding argument graphs in logic

International audienceArgument graphs are a common way to model argumentative reasoning. For reasoning or computational purposes, such graphs may have to be encoded in a given logic. This paper aims at providing a systematic approach for this encoding. This approach relies upon a general, principle-based characterization of argumentation semantics

On Elitist Lifting and Consistency in Structured Argumentation

We address the question of how to lift an ordering over rules to an ordering over arguments (sets of rules) that is well-behaved. It has been shown that so-called elitist lifting may lead to inconsistencies. We give restrictions on the underlying rule-ordering that avoid inconsistency. Then we show that a recently proposed solution – so-called disjoint strict lifting – that was introduced to address conceptual objections, also leads to inconsistency. We show that another recent proposal, telling us to reorder rule-orderings to take argument structure into account before lifting, is able to avoid conceptual problems without leading to any new inconsistencies. We generalise this approach by defining what we call structural rule-orderings and show a correspondence between weakest link and last link lifting of such orderings, which has interesting consequences for the question of consistency. We arrive at our results using a signature-based approach to structured argumentation. Instead of settling on a given framework, such as ASPIC+, we define an argumentation language that allows us to express only those properties of argumentation systems we need to establish our results. This abstract approach simplifies and clarifies the technical work while making our contribution more general

On Elitist Lifting and Consistency in Structured Argumentation

We address the question of how to lift an ordering over rules to an ordering over arguments (sets of rules) that is well-behaved. It has been shown that so-called elitist lifting may lead to inconsistencies. We give restrictions on the underlying rule-ordering that avoid inconsistency. Then we show that a recently proposed solution – so-called disjoint strict lifting – that was introduced to address conceptual objections, also leads to inconsistency. We show that another recent proposal, telling us to reorder rule-orderings to take argument structure into account before lifting, is able to avoid conceptual problems without leading to any new inconsistencies. We generalise this approach by defining what we call structural rule-orderings and show a correspondence between weakest link and last link lifting of such orderings, which has interesting consequences for the question of consistency. We arrive at our results using a signature-based approach to structured argumentation. Instead of settling on a given framework, such as ASPIC+, we define an argumentation language that allows us to express only those properties of argumentation systems we need to establish our results. This abstract approach simplifies and clarifies the technical work while making our contribution more general

Arguments, responsibilities and moral dilemmas in abductive default logic

We assume that an agent is not responsible for rule-induced extensions of its theory about the world; responsibility requires the presence of a choice. This supports the attractive conclusion that responsibility for rule-based agents can only arise when the agent faces a “dilemma” regarding how to apply the rules. Default logic offers precise formulations of this intuition. However, it turns out that existing definitions force us to recognise too many dilemmas when reasoning about rules. Specifically, not all moral conflicts are moral dilemmas; the crucial element of choice is sometimes missing. To address this, we first present a refined definition for normal default theories, before going on to present a generalisation that applies to abstract argumentation frameworks

Arguments, responsibilities and moral dilemmas in abductive default logic

We assume that an agent is not responsible for rule-induced extensions of its theory about the world; responsibility requires the presence of a choice. This supports the attractive conclusion that responsibility for rule-based agents can only arise when the agent faces a “dilemma” regarding how to apply the rules. Default logic offers precise formulations of this intuition. However, it turns out that existing definitions force us to recognise too many dilemmas when reasoning about rules. Specifically, not all moral conflicts are moral dilemmas; the crucial element of choice is sometimes missing. To address this, we first present a refined definition for normal default theories, before going on to present a generalisation that applies to abstract argumentation frameworks