A temporal paraconsistent relational algebra for incomplete and inconsistent information

We construct a framework for natural handling of incomplete and inconsistent information in temporal databases. Central to this framework are structures that we call time-varying paraconsistent relations, which are essentially 4-valued relations that vary over time. For such structures, we present an algebra based on temporal semantics in which there is no explicit manipulation of time indices, yet it is rich enough to express recursive equations as queries. The algebra is a consistent extension of the relational algebra; it supports basic algebraic equivalences, and has a well-defined formal semantics. We also provide many examples of queries expressed in this algebra. To our knowledge, our framework is the first treatment of inconsistent information in the context of temporal databases.