Reactive Kripke models and contrary to duty obligations. Part A: Semantics

This paper introduces a new method for modelling contrary to duty obligations (CTD). Given a contrary to duty obligation structure CTDs presented in English, there is the problem of offering a logical system in which it can be coherently formalised. There are several formal systems in the literature attempting to do so, such as SDL (Standard Deontic Logic), various dyadic operators and other kinds of formalised normative systems. The difficulties encountered by such systems is that they end up with counter intuitive results for some CTD linguistic structures, referred to as paradoxes (for the offered formalising logic). We use reactive Kripke models as the semantics and a reactive extension of SDL, with one additional reactive modality as syntax for such CTD. Reactive Kripke models change their accessibility relation as we move from node to node during the semantic evaluation process. This change is made to correspond to the change implicit in the intuitive meaning of the contrary to duty obligations. The reactive Kripke semantics is stronger semantics than ordinary Kripke models and therefore allows for more fine tuning of our modelling process.