Reactive Kripke Models and Contrary to Duty Obligations

Contrary to duties (CTD) are dealt with in the framework of standard deontic logic (SDL), and ordinary Kripke possible world models. Given a world t, one associates statically a non-empty set I(t) of ideal worlds for t and t Oq (q is obligatory for t) if q holds in all the worlds of I(t). This is a static perception of obligation. If we have to list as t the set of all obligations for the world t then I(t) would be the set of all models of t. The contrary to duty examples have some implicit dynamics in them. It is therefore not surprising that there are problems with the formalisation of various CTD examples within SDL. There are currently in the literature various proposals for solutions, however all are still largely within the STL possible world semantics approach or its extensions, with additional operators or preferential ordering. See footnote 2 below and references [18], [15] and [13]. Reactive Kripke models is a stronger version of possible world semantics, a ording the semantic characterisation of more modal systems (this is a theorem in [1]. They have a dynamic dimension to them. Therefore using this new semantics might simplify existing solutions to CTD problems as well as o er new sharper solutions. Note that this new approach does not necessarily abandon or challenge any of the existing solutions, since ordinary Kripke models are a special case of reactive Kripke models. This is an important point to bear in mind. We can proceed on two fronts.