Making Use of Similarity in Referential Semantics

Similarity is well-known to be a core concept of human cognition, e.g., in categorization and learning. Therefore, expressions of similarity in natural language are of special interest: How to account for their meaning including the results on similarity in Cognitive Science and Artificial Intelligence without abandoning referential semantics? In this paper we will lay out a framework connecting referential semantics to conceptual structures by generalizing the notion of measure functions known in degree semantics from the one-dimensional to the many-dimensional case mapping individuals to points in multi-dimensional attribute spaces. Similarity is then spelled out as indistinguishability with respect to a given set of attributes.