An Integrated Distance for Atoms

In this work, we introduce a new distance function for data representations based on first-order logic (atoms, to be more precise) which integrates the main advantages of the distances that have been previously presented in the literature. Basically, our distance simultaneously takes into account some relevant aspects, concerning atom-based presentations, such as the position where the differences between two atoms occur (context sensitivity), their complexity (size of these differences) and how many times each difference occur (the number of repetitions). Although the distance is defined for first-order atoms, it is valid for any programming language with the underlying notion of unification. Consequently, many functional and logic programming languages can also use this distance.