Extending the $$\rho $$Log Calculus with Proximity Relations

\(\rho \)Log-prox is a calculus for rule-based programming with strategies, which supports both exact and approximate computations. Rules are represented as conditional transformations of sequences of expressions, which are built from variadic function symbols and four kinds of variables: for terms, hedges, function symbols, and contexts. \(\rho \)Log-prox extends \(\rho \)Log by permitting in its programs fuzzy proximity relations, which are reflexive and symmetric, but not transitive. We introduce syntax and operational semantics of \(\rho \)Log-prox, illustrate its work by examples, and present a terminating, sound, and complete algorithm for the \(\rho \)Log-prox expression matching problem.