Printed in Great Britain SPECIALIZATION BY RESTRICTION AND SCHEMA DERIVATIONS

Specialization and inheritance are well known concepts in the area of object oriented modelling and knowledge representation However certain aspects of these concepts lack formal foun dations In particular when properties of di erent classes are semantically related several different semantics are possible for the inherited properties and a choice is necessary Conventional systems impose an a priori solution that supports only one of the possible semantics of inheritance In this paper we present constructs that allow to di erentiate between the possible semantics of inheritance in a formal and sound way Our approach is based on a structured view of the real world and a model for its representation By necessity the model only partly represents the real world Thus reason ing in the model is done with reference to the real world We introduce restriction isa a form of specialization that represents property restriction and demonstrate that it can be a useful conceptual modelling mechanism We employ restriction isa to formally de ne property inheritance Reasoning in our model is done through a number of inference rules that re ect real world constraints These rules allow for sound derivations both at the instance and schema levels At the schema level in particular these rules allow us to relate inherited properties to other properties through restriction isa and isa relations Such relations not only give useful information about the inherited properties but also re ne the values of these properties Copyright c Elsevier Science Ltd