Semantic Networks as Abstract Data Types

system which is shown to be noetherian and confluent. The metanet is correct, in the sense that terms built of operations and individuals from the domain of semantic networks,i.e. describing networks can be reduced into an equivalent minimal genera­ ting expression which is not further reduc­ ible and which contains only constructors. II SPECIFICATION OF A METANET Because of the abstraction from con­ crete types for nodes and edges, we can define operations on nodes and edges inde­ pendently from their types. So we are able to examine general characteristics of se­ mantic networks. This leads to production schemata instead of productions of the re­ write system, i.e. the axiomatic definition can be conceived as a meta-description of a semantic net, from which the axiomatiza-tion of concrete nets can be derived by in­ stantiation of concrete types for all oc­ currences of type variables. For example, node types could be "concept" and "instance" edge types could be "isa", "subset-of", "object-of", "agent".By means of this ab­ straction we get an axiomatic definition of the abstract data type "metanet" by 35 axioms which are easy to surrey. Some of the axioms are provided with conditions, enclosed in {...}, wich restrict the ap­ plicability of the productions. We now present the specification of the abstract data type "metanet". This specification is based on the abstract data types "boolean" and "set", "set" con­ sists of the operations: EMPTYSET, ISEMPTY-A meta-description of semantic networks as abstract data types is given by a set of 35 production schemata. With this schemata it is possible to specify all types of semantic networks as abstract data types. By instantiation of concrete types for nodes and edges as semantic primitives we get from the meta-description axiomatic definitions of arbi­ trary types of semantic networks as ab­ stract data types. The production schemata of the meta-description can be shown to be noetherian and confluent. Each term describing a semantic network can be reduced to an equivalent minimal generating expression. I INTRODUCTION Semantic networks are frequently used in NL-systems as a means for knowledge re­ presentation. There is a great number of different types of semantic networks which demonstrates their qualification for the purpose of knowledge representation. In (Barr and Feigenbaum, 1981), knowledge re­ presentation is conceived as data struc­ tures together with interpretative opera­ tions. We adopt this interpretation for se­ mantic networks and describe them by means of the …