Sedatalog: A Set Extension of Datalog

In this paper we propose an extension, SEDatalog, of Datalog so that sets can be constructed naturally in logic programming. In SEDatalog, sets can be defined by statements so it has a strong capability in creating sets, and we can use sets in SEDatalog exactly in the way we use them in mathematics or other fields. With the notion of ”order” introduced in this paper, confusions among set construction levels can be avoid in SEDatalog. Three deductive rules are also introduced in this paper, which make SEDatalog being able to do deductions and to make programs even when sets are involved in deductions. The syntactical description and the semantic interpretation of SEDatalog are comprehensively discussed in detail. The soundness and completeness theorem of SEDatalog is proved, which provides a solid foundation of SEDatalog.