Consistency of Rules and Norms

This paper develops the theory that a set of rules is consistent if it is not possible that (1) the conditions of the rules in the set are all satisfied (2) there is no exception to either one of the rules, and (3) the consequences of the rules are incompatible. To this purpose the notion of consistency is generalised to make it cover rules and is relativised to a background of constraints. It is argued that a similar theory is also useful to characterise the consistency of deontic sentences of the ought-to-do type. The theory about rule consistency is formalised by means of Rule Logic, in which rules are treated as constraints on the possible worlds in which they exist. Rule Logic itself is introduced by giving a model-theory for it. It is characterised by means of constraints on worlds that are possible according to Rule Logic. The formal theory is refined by disallowing ungrounded exceptions to rules. To that purpose an additional constraint is imposed on worlds that are possible according to Rule Logic.