A Non-Standard Temporal Deductive Database System

A new temporal deductive database system supporting a non-standard model of time is introduced. It consists of Non-standard Temporal Datalog (nstl) and Non-standard Temporal Relational Algebra (nstra). The time line consists of non-standard reals that are of the form 〈r, z〉, where r ∈ R and z ∈ Z, using the natural order. Each real r determines a macro-instant, and each pair 〈r, z〉 defines a micro-instant. The set of macro-instants forms a dense order, thereby allowing different relations to be valid at different moments, with independent rates of evolution. The micro-instants ensure that all intervals are closed, thereby simplifying the semantics. At the same time, it becomes possible to define a discrete memory operator. The nstl language is an extension of Datalog in which the fact base is augmented with interval timestamps and in which rules are an extension of generalized Horn clauses that allow a memory operator “;” and allow timestamped atoms in the body. The nstra language is a pointwise extension of the relational algebra over the time line. To do this, three temporal operators are added to the relational algebra.