# Naive Tables

**DOI:**https://doi.org/10.1007/978-1-4614-8265-9_1252

## Synonyms

Extended relations; Relations with marked nulls

## Definition

The simplest way to incorporate unknown values into the relational model, is to allow *variables*, in addition to *constants*, as entries in the columns of relations. Such constructs are called *tables*, instead of *relations*. A table is an incomplete database, and *represents a set of complete databases*, each obtained by substituting all variables with constants. Different occurrences of the same variable (marked null) are substituted with the same constant. The substitution is thus a function from the variables and constants, to the constants, such that the function is identity on the constants. A table *T* then represents the set of relations, denoted *rep*(*T*), defined as {*v*(*T*) : *v* is a valuation}. Then the *certain answer* to a query *q* on a table *T*, denoted *sure*(*q*, *T*) is the set of tuples that occur in every answer obtained by applying the query to every database in *rep*(*T*). In other words, the certain answer to *q* on *T* is *sure*(*q*,...

## Recommended Reading

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