The principle-based approach is a methodology to classify and analyse argumentation semantics. In this paper we classify seven of the main alternatives for argumentation semantics using a set of new robustness principles. These principles complement Baroni and Giacomin’s original classification and deal with the behaviour of a semantics when the argumentation framework changes due to the addition or removal of an attack between two arguments. We distinguish so-called persistence principles and monotonicity principles, where the former deal with the question of (...) whether a labelling or extension of an argumentation framework under a given semantics persists after a change, and the latter with the question of whether new labellings or extensions are created after a change. We furthermore show in which sense labelling-based and extension-based semantics lead to subtly different principles and results. Our results can be used for choosing a semantics for a particular application, or to guide the search for new argumentation semantics, but they have been used also in the design of algorithms. (shrink)

ABSTRACTThis paper studies abduction in abstract argumentation frameworks. Given an argument, an agent verifies whether the argument is justified or not in its argumentation framework. If the argument is not justified in the argumentation framework, the agent seeks conditions to explain the justification state by hypothesising arguments in the universal argumentation framework. We formulate such abductive reasoning in argumentation semantics and provide its computation in logic programming. We also apply abduction to enforcement and simple dialogue games in argumentation frameworks.

In this article, we first study abduction in human dialogues. Given an utterance, objective abduction produces a hearer’s belief that could explain the utterance, while subjective abduction produces a hearer’s belief that could explain the belief state of a speaker. Different types of abduction are formulated using propositional epistemic logic. We next consider conversational implicature used as pragmatic inference in speech acts. Two conflicting implicatures, Q-implicature and I-implicature, are formulated and contrasted with abduction. We also argue how speakers could use (...) abduction or conversational implicature for the purpose of misleading hearers. (shrink)

In Hollis’ paradox, A and B each chose a positive integer and whisper their number to C. C then informs them, jointly, that they have chosen different numbers and, moreover, that neither of them are able to work out who has the greatest number. A then reasons as follows: B cannot have 1, otherwise he would know that my number is greater, and by the same reasoning B knows that I don’t have 1. But then B also cannot have 2, (...) otherwise he would know that my number is greater (since he knows I don’t have 1). This line of reasoning can be repeated indefinitely, effectively forming an inductive proof, ruling out any number – an apparent paradox. In this paper we formalise Hollis’ paradox using public announcement logic, and argue that the root cause of the paradox is the wrongful assumption that A and B assume that C’s announcement necessarily is successful. This resolves the paradox without assuming that C can be untruthful, or that A and B are not perfect reasoners, like other solutions do. There are similarities to the surprise examination paradox. In addition to a semantic analysis in the tradition of epistemic logic, we provide a syntactic one, deriving conclusions from a set of premises describing the initial situation – more in the spirit of the literature on Hollis’ paradox. The latter allows us to pinpoint which assumptions are actually necessary for the conclusions resolving the paradox. (shrink)