The semantics of inheritance networks
Michael Kifer, David Scott Warren, Thirunarayan Krishnaprasad · 1989
The notion of inheritance is fundamental to Knowledge Representation Systems. Inheritance networks are structures employed to represent prototypical knowledge. Reasoning with inheritance networks has been ad hoc in the past because their semantics were not well-understood. Only recently have researchers tried to provide a semantics for them. This has been done either through a translation into a general logical formalism or by special path-based techniques. The former approach requires the specification of an algorithmic transformation of the network into a set of sentences in a logic language. The intuitions about inheritance are captured indirectly through the semantics of the logic language. The user must know the logical formalism and the details of the translation algorithm to understand the meaning of the network. In the second approach, the semantics is given by characterizing sets of inheritance paths in the network. This specification is very complex, and has subtle side effects making it difficult for the user to fully understand the semantics. This dissertation introduces a general framework for specifying declarative semantics of inheritance networks directly in terms of the network. This provides a model-theoretic specification of the meaning that is easy to understand and use. Furthermore, this framework gives a uniform way to compare different proposals for inheritance. To study the formal properties of credulous and skeptical theory of inheritance, I developed logical semantics for these networks. The credulous theory is based on the circumscriptive translation. For the skeptical theory, I have proposed an evidence-based logic obtained by amalgamating concepts from logic-programming and multi-valued logics. This dissertation generalizes traditional networks to so-called preferential networks. This allows specification of information to resolve ambiguity that arises because of the topology of the network, but which is not inherent in the problem being modelled. I also show that the understanding of inheritance as the flow of individuals up the network to acquire properties better captures intuitions about inheritance than the view of properties flowing downwards. My theories exhibit locality and form the basis for the design and implementation of efficient inheritance algorithms.