Abstract

. In this paper we introduce the two-phase deontic logic 2dl. The preference-based semantics of 2dl is based on an explicit preference ordering between worlds, representing different degrees of ideality. The preference ordering can be used in two ways to evaluate formulas, which we call ordering and minimizing. Ordering uses all preference relations between relevant worlds, whereas minimizing uses the most preferred worlds only. We show that ordering corresponds to the inference pattern strengthening of the antecedent and the conjunction rule for the consequent, and minimizing to the inference pattern weakening of the consequent and the disjunction rule for the antecedent. Moreover, we show that in several problems like the notorious contrary-to-duty paradoxes ordering and minimizing have to be combined to obtain the desirable conclusions, and that in a dyadic deontic logic this can only be done in a so-called two-phase deontic logic. In the first phase the preference ordering is const...

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