A Set Extension of Prolog: The Definitions

In this paper we propose a set extension of Prolog, SEProlog, so that sets can be constructed in logic programming. In SEProlog sets are defined intensively, so it has a strong capability in creating sets. To avoid any possible confusions in the set construction levels, a basic notion "order" which is assigned to every set and formula of SEProlog is introduced with which such paradoxes as "the set of all sets" or "a set containing itself" will not be possible to be constructed in our proposal even when sets in it are defined intensively. Three deductive rules are also introduced in this paper, which make SEProlog strong in deductions and programming even when sets are involved in deductions.