On Temporal Deductive Databasesy MEHMET A. ORGUN
Department of Computing, Macquarie University Sydney, NSW 2109, Australia Tel: +61 (0)2 805-9916, Fax: +61 (0)2 805-8983 E-mail:
[email protected] ABSTRACT This paper introduces a temporal deductive database system featuring a logic programming language and an algebraic front-end. The language, called Temporal Datalog, is an extension of Datalog based on a simple temporal logic with two temporal operators, namely first and next. Programs of Temporal Datalog are considered as temporal deductive databases, specifying temporal relationships among data and providing base relations to Tra expressions. The minimum model of a given Temporal Datalog program is regarded as the temporal database the program models intensionally. The algebraic front-end, called Tra, is a point-wise extension of the relational algebra upon the set of natural numbers. When needed during the evaluation of Tra expressions, slices of temporal relations over intervals can be retrieved from a given temporal deductive database by bottom-up evaluation strategies. A modular extension of Temporal Datalog is also proposed, through which temporal relations created during the evaluation of Tra expressions may be fed back to the deductive part for further manipulation. Modules therefore enable the algebra to have full access to the deductive capabilities of Temporal Datalog, and to extend it with non-standard algebraic operators. The paper also shows that the temporal operators of Tra can be simulated in Temporal Datalog by program clauses.
Keywords: Temporal Databases, Temporal Algebras, Deductive Databases, Logic Pro-
gramming, Temporal Logic, Declarative Semantics, Modules.
This is a substantially extended and revised version of the paper \A relational algebra as a query language for Temporal Datalog", which appeared in A. Min Tjoa and Isidro Ramos, editors, Proceedings of DEXA'92: The Third International Conference on Database and Expert Systems Applications, Valencia, Spain, September 2{4, 1992. Springer-Verlag, pp.276{281. y
1 Introduction This paper introduces a temporal deductive database system featuring a logic programming language and an algebraic front-end. The language, which we call Temporal Datalog, is an extension of Datalog [6, 30] based on a simple temporal logic with two temporal operators, namely first and next. The ow of time in the temporal logic is modeled by the set of natural numbers with its usual ordering relation . The de ned fby[.] operator is very useful, so we employ it as a native operator in Tra.
Example 6 Suppose that a 10% overall salary increase is planned starting at month t and the management wants to study its long term e ects on the company. The temporal database is now extended with a new employee relation, say proj-emp, modeling the salary increase starting at month t in order to keep the de nition of the original emp relation intact. Supposing the emp relation is provided for all moments in time (for the future as well), we can de ne the proj-emp relation as follows: t
next( ) proj-emp(Name,Dept,Salary)
