An Extension of Semantic Schemas to Represent Multiple Meanings

Various applications of semantic schemas were presented in logical representation of knowledge, knowledge management; distributed knowledge and reasoning by analogy ([8], [11], [12]). A semantic schema is an abstract structure that uses a Peano theta-algebra. Only one operation symbol, denoted by B, is used to build this algebra. In this paper we consider a set circle minus = {theta(1), . . . , theta(n)} of n operation symbols and we introduce the concept of generalized schema based on a Peano circle minus-algebra. For the particular case n = 1 we obtain the concept of semantic schema. Both the formal computations and the semantic computations for this extension are described. The new structure allows its to use multiple meanings for the entities of a generalized schema in comparison with a semantic schema, where each entity has only one meaning. This aspect is exemplified in a separate section.