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Abstract: The concept of “ideal semantics” has been promoted as an alternative basis for skeptical reasoning within abstract argumentation settings. Informally, ideal acceptance not only requires an argument to be skeptically accepted in the traditional sense but further insists that the argument is in an admissible set all of whose arguments are also skeptically accepted. The original proposal was couched in terms of the so-called preferred semantics for abstract argumentation. We argue, in this paper, that the notion of “ideal acceptability” is applicable to arbitrary semantics and justify this claim by showing that standard properties of classical ideal semantics, e.g. unique status, continue to hold in any “reasonable” extension-based semantics. We categorise the relationship between the divers concepts of “ideal extension w.r.t. semantics σ” that arise and we present a comprehensive analysis of algorithmic and complexity-theoretic issues. In addition we offer further support for the view that “ideal semantics” ought to be seen as a generic property by presenting and analysing the forms that these might take within value-based argumentation frameworks. [Copyright &y& Elsevier]

When modeling a decision problem using the influence diagram framework, the quantitative part rests on two principal components: probabilities for representing the decision maker''s uncertainty about the domain and utilities for representing preferences. Over the last decade, several methods have been developed for learning the probabilities from a database. However, methods for learning the utilities have only received limited attention in the computer science community.A promising approach for learning a decision maker''s utility function is to take outset in the decision maker''s observed behavioral patterns, and then find a utility function which (together with a domain model) can explain this behavior. That is, it is assumed that decision maker''s preferences are reflected in the behavior. Standard learning algorithms also assume that the decision maker is behavioral consistent, i.e., given a model of the decision problem, there exists a utility function which can account for all the observed behavior. Unfortunately, this assumption is rarely valid in real-world decision problems, and in these situations existing learning methods may only identify a trivial utility function. In this paper we relax this consistency assumption, and propose two algorithms for learning a decision maker''s utility function from possibly inconsistent behavior; inconsistent behavior is interpreted as random deviations from an underlying (true) utility function. The main difference between the two algorithms is that the first facilitates a form of batch learning whereas the second focuses on adaptation and is particularly well-suited for scenarios where the DM''s preferences change over time. Empirical results demonstrate the tractability of the algorithms, and they also show that the algorithms converge toward the true utility function for even very small sets of observations. [Copyright &y& Elsevier]