Referential integrity is a property of data stating that all its references are valid. In the context ofrelational databases, it requires that if a value of one attribute (column) of arelation (table) references a value of another attribute (either in the same or a different relation), then the referenced value must exist.^[1]

For referential integrity to hold in a relational database, any column in a basetable that is declared aforeign key can only contain either null values or values from a parent table'sprimary key or acandidate key.^[2] In other words, when a foreign key value is used it must reference a valid, existing primary key in the parent table. For instance, deleting a record that contains a value referred to by a foreign key in another table would break referential integrity. Somerelational database management systems (RDBMS) can enforce referential integrity, normally either by deleting the foreign key rows as well to maintain integrity, or by returning an error and not performing the delete. Which method is used may be determined by a referential integrity constraint defined in adata dictionary.

The adjective 'referential' describes the action that aforeign key performs, 'referring' to a linked column in another table. In simple terms, 'referential integrity' guarantees that the target 'referred' to will be found. A lack of referential integrity in a database can lead relational databases to return incomplete data, usually with no indication of an error.

Aninclusion dependency over two (possibly identical) predicates${\displaystyle R}$ and${\displaystyle S}$ from a schema is written${\displaystyle R[A_1,...,A_n]\subseteq S[B_1,...,B_n]}$, where the${\displaystyle A_i}$,${\displaystyle B_i}$ are distinct attributes (column names) of${\displaystyle R}$ and${\displaystyle S}$. It implies that the tuples of values appearing in columns${\displaystyle A_1,...,A_n}$ for facts of${\displaystyle R}$ must also appear as a tuple of values in columns${\displaystyle B_1,...,B_n}$ for some fact of${\displaystyle S}$.

Such constraint is a particular form oftuple-generating dependency (TGD) where in both the sides of the rule there is only one relational atom.^[3] Infirst-order logic it is expressible as${\displaystyle \mathrm{\forall }\overrightarrow{x},\overrightarrow{y}.(R(\overrightarrow{x},\overrightarrow{y})\to \mathrm{\exists }\overrightarrow{z}.S(\overrightarrow{x},\overrightarrow{z}))}$, where${\displaystyle \overrightarrow{x}}$ is the vector (whose size is${\displaystyle n}$) of variables shared by${\displaystyle R}$ and${\displaystyle S}$, and no variable appears multiple times neither in the TGD's body nor in its head.

Logical implication between inclusion dependencies can be axiomatized by inference rules^[4]: 193and can bedecided by aPSPACE algorithm. The problem can be shown to bePSPACE-complete by reduction from the acceptance problem for alinear bounded automaton.^[4]: 196 However, logical implication between dependencies that can be inclusion dependencies orfunctional dependencies is undecidable by reduction from theword problem formonoids.^[4]: 199

Declarative referential integrity (DRI) is one of the techniques in theSQL database programming language to ensure data integrity.

A table (called the referencing table) can refer to a column (or a group of columns) in another table (the referenced table) by using aforeign key. The referenced column(s) in the referenced table must be under a unique constraint, such as aprimary key. Also, self-references are possible (not fully implemented in MS SQL Server though^[5]). Oninserting a newrow into the referencing table, therelational database management system (RDBMS) checks if the entered key value exists in the referenced table. If not, no insert is possible. It is also possible to specify DRI actions onUPDATE andDELETE, such as CASCADE (forwards a change/delete in the referenced table to the referencing tables), NO ACTION (if the specific row is referenced, changing the key is not allowed) or SET NULL / SET DEFAULT (a changed/deleted key in the referenced table results in setting the referencing values to NULL or to the DEFAULT value if one is specified).^[6]

InMicrosoft SQL Server the term DRI also applies to the assigning of permissions to users on adatabase object. Giving DRI permission to a database user allows them to add foreign key constraints on a table.^[7]

• Null pointer dereferencing
• Dangling pointer
• Data integrity
• Domain/key normal form
• Entity integrity
• Functional dependency
• Propagation constraint
• Surrogate key
• Slowly changing dimension

• DRI versus Triggers (archived)

• Database management systems
• Data quality

• Articles with short description
• Short description is different from Wikidata