Tuple Relational Calculus for Paraconsistent Databases

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Abstract

A paraconsistent database is one in which information may be incomplete and/or inconsistent. A data model that does not attempt to eliminate such incompleteness or inconsistency, but rather is capable of functioning in their presence, has recently been developed. In this paper, we present a 4-valued tuple relational calculus for posing queries to paraconsistent databases based on that model. The syntax of our calculus is similar to that of the regular 2-valued relational calculus on ordinary relational databases, but our new 4-valued semantics makes it a useful querying tool for applications containing incomplete and inconsistent information. Moreover, as the model (out of necessity) freely permits infinite relations, the issue of safety of calculus expressions, that is so important in 2-valued systems, is not relevant any more.