Which property ensures that information decomposed across many relations can be reconstructed using natural joins?

The property that ensures that information decomposed across many relations can be reconstructed using natural joins is called "Lossless Join Property".

Here are the steps to explain this property:

1. In the context of relational databases, decomposition refers to the process of breaking down a table into two or more tables. This is often done to normalize the database and eliminate redundancy.

2. The Lossless Join Property is a fundamental property of relational database theory. It ensures that when a database is decomposed, no information is lost.

3. Specifically, the Lossless Join Property guarantees that the natural join of the decomposed tables will yield the original table. A natural join is a type of join that combines two tables based on their common attributes.

4. For example, if we have a table 'A' with attributes (X, Y, Z) and we decompose it into two tables 'B' (X, Y) and 'C' (Y, Z), the natural join of 'B' and 'C' on the common attribute 'Y' will give us back the original table 'A'.

5. This property is crucial for maintaining the integrity of the data in a relational database. Without it, decomposing and then reconstructing a table could result in a loss of information, which could lead to inaccurate query results and other problems.