Similarity relational calculus and its reduction to a similarity algebra

Traditional database query languages are based on set theory and crisp logic. Many applications, however, need similarity or retrieval-like queries producing results with truth values from the interval [0, 1]. Such truth values can be regarded as continuous membership values of tuples expressing how strongly a query is matched. Formulating queries by applying existing similarity relational algebras means to express the user's need in a procedural manner. In order to support a declarative way of formulating queries, we generalize the classical relational domain calculus by incorporating fuzzy operations and user weights. Besides defining syntax and semantics we show how to map any calculus expression onto a corresponding similarity algebra expression. In this way, we present a theoretical foundation for a declarative query language combining retrieval functionality and traditional relational databases.