# Chapter 5 Relational Model Concepts Dr. Bernard Chen Ph.D. University of Central Arkansas.

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Chapter 5 Relational Model Concepts Dr. Bernard Chen Ph.D. University of Central Arkansas

Relational Model Concepts A Relation is a mathematical concept based on the ideas of sets The model was first proposed by Dr. E.F. Codd of IBM Research in 1970 in the following paper: "A Relational Model for Large Shared Data Banks," Communications of the ACM, June 1970 The above paper caused a major revolution in the field of database management and earned Dr. Codd the coveted ACM Turing Award

Outline Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations Relational Model Constrains and Relational Database Schemas Update Operations, Transactions, and Dealing with Constrain Violations

Relational Model Concepts The relational model represents the database as a collection of relations Each relation resembles a table of values When a relation is thought of as a table of values, each row in the table represents a collection of related data values

Formal Terminology A row is called a tuple A column header is called an attribute The table is called relation

Domain A Domain D is a set of atomic values. Atomic means that each value in the domain is indivisible as far as the relational model is concerned It means that if we separate an atomic value, the value itself become meaningless, for example: SSN Local_phone_number Names Employee_ages

Relation Schema Relation Schema R, denoted by R(A1, A2,…, An), is made up of relation name R and a list of attributes A1, A2, …,An Each attribute Ai is the name of a role played by some domain D in the relation schema R. D is called the domain of Ai and is denoted by dom(Ai) R is called the name of the relation The degree of a relation is the number of attributes n of its relation schema

Formal Definitions Formally, Given R(A1, A2,.........., An) r(R)  dom (A1) X dom (A2) X....X dom(An) R(A1, A2, …, An) is the schema of the relation R is the name of the relation A1, A2, …, An are the attributes of the relation

Formal Definitions Let R(A1, A2) be a relation schema: Let dom(A1) = {0,1} Let dom(A2) = {a,b,c} Then: dom(A1) X dom(A2) is all possible combinations: {,,,,, } The relation state r(R)  dom(A1) X dom(A2)

Definition Summary Informal TermsFormal Terms TableRelation Column HeaderAttribute All possible Column Values Domain RowTuple Table DefinitionSchema of a Relation Populated TableState of the Relation

Outline Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations Relational Model Constrains and Relational Database Schemas Update Operations, Transactions, and Dealing with Constrain Violations

Ordering Ordering of Tuples is a Relation a relation is defined as a set of tuples. Mathematically, elements of a set have NO order among them The ordering indicates first, second, ith, and last records in the file Hence, the following two relations are identical

Identical Relations

Values in the Tuples Each value in a tuple is an atomic value Hence, composite and multi-valued attributes are not allowed This model is sometimes called the flat relational model Much of the theory behind the relational model was developed with this assumption, which is called first normal form assumption

Null in tuples An important concept is that if NULL values, which are used to represent the values of attributes that may be unknown or may not apply to a tuple

Relational Model Notation An attribute A can be qualified with the relation name R to which it belongs by using the dot notation R.A For example, STUDENT.Name or STUDENT.Age

Outline Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations Relational Model Constrains and Relational Database Schemas Update Operations, Transactions, and Dealing with Constrain Violations

Domain Constrains Each attribute A must be an atomic value from the dom(A) The data types associated with domains typically include standard numeric data type for integers, real numbers, Characters, Booleans, fix-length strings, time, date, money or some special data types

Key Constrains A relation is defined as a set of tuples By definition, all elements of a set are distinct This means that no two tuples can have the same combination of values for all their attributes Superkey: a set of attributes that no two distinct tuples in any state r of R have the same value Every relation has at least one default superkey – the set of all its attributes

Key Constrains A superkey can have redundant attributes, so a more useful concept is that of a KEY which has no redundancy Key satisfied two constrains: Two distinct tuple in any state of the relation cannot have identical values for the attributes in the key It is a minimal superkey

Key Constrains For example, consider STUDENT relation The attribute set {SSN} is a key of STUDENT because no two student can have the same value for SSN Any set of attributes that includes SSN – for example {SSN, Name, Age} – is a superkey

Key Constrains In general, a relation schema may have more than one key, in this case, each of the key is called a candidate key Example: Consider the CAR relation schema: CAR(State, Reg#, SerialNo, Make, Model, Year) CAR has two keys: Key1 = {State, Reg#} Key2 = {SerialNo} Both are also superkeys of CAR {SerialNo, Make} is a superkey but not a key (because it is not minimum).

CAR table with two candidate keys – LicenseNumber chosen as Primary Key

Key Constrains If a relation has several candidate keys, one is chosen arbitrarily to be the primary key. Example: Consider the CAR relation schema: CAR(State, Reg#, SerialNo, Make, Model, Year) We chose SerialNo as the primary key The primary key value is used to uniquely identify each tuple in a relation Provides the tuple identity Also used to reference the tuple from another tuple General rule: Choose as primary key the smallest of the candidate keys (in terms of size) Not always applicable – choice is sometimes subjective

Key Constrains and Constrains on NULL values Another constraint on attributes specifies whether NULL value are or are not permitted For example, if every STUDENT tuple must have a valid, non-NULL value for the Name attribute, then Name of STUDENT is constrained to be NOT NULL

Relational Database Schema Relational Database Schema: A set S of relation schemas that belong to the same database. S is the name of the whole database schema S = {R1, R2,..., Rn} R1, R2, …, Rn are the names of the individual relation schemas within the database S Following slide shows a COMPANY database schema with 6 relation schemas

COMPANY Database Schema

Entity Integrity Entity Integrity: The primary key attributes (PK) of each relation schema R in S cannot have null values in any tuple of r(R). This is because primary key values are used to identify the individual tuples. t[PK]  null for any tuple t in r(R) If PK has several attributes, null is not allowed in any of these attributes Note: Other attributes of R may be constrained to disallow null values, even though they are not members of the primary key.

Referential Integrity Constraint Referential Integrity Constraint is specified between two relations and is used to maintain the consistency among tuples in the two relations Informally define the constrain: a tuple in one relation must refer to an existing tuple in that relation For example, the Dno in EMPLOYEE gives the department number for which each employee works, this number must match the Dnumber value in DEPARTMENT

Referential Integrity Constraint Tuples in the referencing relation R1 have attributes FK (called foreign key attributes) that reference the primary key attributes PK of the referenced relation R2. A tuple t1 in R1 is said to reference a tuple t2 in R2 if t1[FK] = t2[PK].

Displaying a relational database schema and its constraints Each relation schema can be displayed as a row of attribute names The name of the relation is written above the attribute names The primary key attribute (or attributes) will be underlined A foreign key (referential integrity) constraints is displayed as a directed arc (arrow) from the foreign key attributes to the referenced table Can also point the the primary key of the referenced relation for clarity Next slide shows the COMPANY relational schema diagram

Referential Integrity Constraints for COMPANY database

Other Types of Constraints Semantic Integrity Constraints: based on application semantics and cannot be expressed by the model per se Example: “the max. no. of hours per employee for all projects he or she works on is 56 hrs per week” A constraint specification language may have to be used to express these

Outline Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations Relational Model Constrains and Relational Database Schemas Update Operations, Transactions, and Dealing with Constrain Violations

Modification and Updates In this section, we concentrate on the database Updates and Modification There are threee basic operation: Insert, Delete and Modify Insert is used to insert a new tuple or tuples in a relation Delete is used to delete tuples Update (or Modify) is used to change the values of some attributes

Modification and Updates Insert: insert new element with specify all related attributes Delete: delete an element by giving Relation name and key of the tuple Modify: modify a value by giving a relation name, Key of the target tuple and attribute to modify

Possible violations for each operation INSERT may violate any of the constraints: Domain constraint: if one of the attribute values provided for the new tuple is not of the specified attribute domain Key constraint: if the value of a key attribute in the new tuple already exists in another tuple in the relation Referential integrity: if a foreign key value in the new tuple references a primary key value that does not exist in the referenced relation Entity integrity: if the primary key value is null in the new tuple

Insert Example Insert into EMPLOYEE Insert

Possible violations for each operation DELETE may violate only referential integrity: If the primary key value of the tuple being deleted is referenced from other tuples in the database Can be remedied by several actions: RESTRICT, CASCADE, SET NULL RESTRICT option: reject the deletion CASCADE option: propagate the new primary key value into the foreign keys of the referencing tuples SET NULL option: set the foreign keys of the referencing tuples to NULL One of the above options must be specified during database design for each foreign key constraint

Delete Example Delete the EMPLOYEE tuple with Ssn=‘999887777’ Delete the EMPLOYEE tuple with Ssn=‘333445555’ Delete the EORKS_ON tuple with Essn=‘999887777’ and Pno=10 (accepted)

Possible violations for each operation UPDATE may violate domain constraint and NOT NULL constraint on an attribute being modified Any of the other constraints may also be violated, depending on the attribute being updated: Updating the primary key (PK): Similar to a DELETE followed by an INSERT Need to specify similar options to DELETE Updating a foreign key (FK): May violate referential integrity Updating an ordinary attribute (neither PK nor FK): Can only violate domain constraints

Update Example Update the salary of EMPLOYEE tuple with Ssn=‘999887777’ to 2800 (Accept) Update the Dno of the EMPLOYEE tuple with Ssn=‘999887777’ to 1 (Accept) Update the Dno of the EMPLOYEE tuple with Ssn=‘999887777’ to 7 Update the Ssn of the EMPLOYEE tuple with Ssn=‘999887777’ to ‘987654321’

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