On generation of cumulative inference operators by default deduction rules

The paper deals with the question how a cumulative inference operator can be generated by default deduction rules. After discussing the “classical” ways (i.e. the sceptical and the credulous definition as well as Brewka's approach) we propose a new approach, the socalled codiagonal generation of cumulative inference operator by default deduction rules. This approach gives the possibility to generalize the abstract theory of monotonic inference operators (due to Tarski, Birkhoff, Hall and Schmidt) to the case considered. In particular, it allows to formulate simple conditions on the given system of default deduction rules so that the generated inference operator is cumulative. Some other methods to generate inference operators by default deduction rules, similiar to the “generating philosophy” used, are described in the last section.