On Temporal Deductive Databasesy

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. y 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.