Publication Date



Technical Report: UTEP-CS-10-18

To appear in Proceedings of the Symposium on Constructive Mathematics in Computer Science, Lexington, Kentucky, October 25-26, 2010, Springer Lecture Notes in Computer Science.


Constructive mathematics, mathematics in which the existence of an object means that that we can actually construct this object, started as a heavily restricted version of mathematics, a version in which many commonly used mathematical techniques (like the Law of Excluded Middle) were forbidden to maintain constructivity. Eventually, it turned out that not only constructive mathematics is not a weakened version of the classical one -- as it was originally perceived -- but that, vice versa, classical mathematics can be viewed as a particular (thus, weaker) case of the constructive one. Crucial results in this direction were obtained by M. Gelfond in the 1970s. In this paper, we mention the history of these results, and show how these results affected constructive mathematics, how they led to new algorithms, and how they affected the current activity in logic programming-related research.