On the Declarative Semantics of Inheritance Networks

Usually, semantics of inheritance networks is specified indirectly through a translation into one of the standard logical formalisms. Since such translation involves an algorithmic aspect, which is usually complex, these approaches to inheritance are not truly declarative. We provide a general framework for specifying a direct semantics of inheritance networks. Because the networks are not expressive enough to capture all intuitions behind inheritance, a number of significantly different semantics have been proposed. Our approach allows us to give direct semantics to a number of different proposals found in the literature, and clarifies the relationships among them. It also provides a yardstick for measuring adequacy of translation into logical formalisms of various intuitions about inheritance. 1 Introduction Inheritance networks represent individuals, classes and properties. For efficient representation and determination of properties of individuals, these networks have evolved from simple property lists to class-subclass hierarchies to multiple inheritance networks. Any realistic representation of the real-world knowledge must necessarily allow representation of exceptions. For instance, typically mammals are nonflyers. Bats are exceptional mammals that normally fly. But dead bats do not fly. In general, inheritances from subclasses must dominate over inheritances from classes in the case of a conflict. The representation language should also allow expression of preferential inheritance of a property from a class over inheritance from another class. For instance, given that man is an omnivore, that is, man is both a her-bivore and a carnivore, one must be able to infer that men have canines. Even though herbivores typically do not possess canines, man "inherits" them because he is a carnivore. Providing a satisfactory semantics to nonmonotonic multiple inheritance networks poses a significant intellectual challenge, and a number of different proposals have appeared in the literature. Normally, the semantics is given through a translation into a logical formal-However , none of these approaches can be regarded as truly declarative. The problem is that an algorithmic transformation from inheritance networks to some logical formalism is given, and only then its semantics described in terms of this formalism. Depending on the conceptual difficulty of the algorithmic part, the claim of "declara-tiveness" of each specific approach is unfounded to a different degree. In addition, these approaches are usually complex and it is not clear how the different semantics relate to each other. In this paper, we provide a general framework for specifying declarative semantics of inheritance networks directly. From the users point of …