Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Disentangling Intertemporal Substitution and Risk Aversion under the Expected Utility Theorem

A disturbing feature of the conventional objective function for intertemporal decisions under uncertainty is that the agent's attitudes toward intertemporal substitution and risk aversion are entangled. This paper shows that, in contrast to common perception, the two attitudes can be completely disentangled under the expected utility theorem (EUT) by modeling each of them successively in two steps. The conventional form is nested as a special case where the functions describing the two attitudes are identical. The proposed framework requires only the standard axioms of the EUT, in addition to a regulatory assumption. It is flexible in accommodating different combinations of the two attitudes, indifferent to the timing of resolution of uncertainty, intuitive to interpret, and extendable to multiple goods. The objective function under the proposed framework is time inconsistent according to Strotz's (1955) definition. I argue that Strotz's notion of time consistency is misguided. It is constructed based on a priori assumption that the agent should continuously forget history as time progresses. But this means the agent is either chronically amnesiac or self-contradictory. To be truly consistent, the agent should have one and only one objective function, determined at birth, throughout his entire life. As history unfolds, the agent updates his information set, but not his objective function