Prohairetic Deontic Logic (PDL)

摘要

In this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based dyadic deontic logic. An obligation '#alpha# should be (done) if #beta# is (done)' is true if (1) no #alpha##under epistemic interpretations of the operator square. Relative to a modal system S, we give three characterizations of minimality of a formula #phi# and give conditions under which these characterizations are equivalent. We then argue that rather than usign bisimulations, it is more appropriate to base information orders on Ehrenfeucht-Fraiesse games to come up with a satisfactory analysis of minimality. Moving to the realm of epistemic logics, we show that for one of these information orders almost all systems trivialize, i.e., either all or no formulas are honest. The other order is much mroe promising as it permits to mini