Relational Calculus: Predicate, Tuple and Domain, Slides of Database Management Systems (DBMS)

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Relational Calculus

Introduction

• Relational Calculus is a formal non-procedural language that uses predicates.

Predicate Calculus

• Predicate – A truth-valued function with arguments.
• Example:

{ x | P (x) }

“For the set of all x such that P is true for x .”

Predicate Calculus

• Expressions are constructed from well-formed formulas (WFFs).
• WFF – An expression composed of atomic predicates.
• Predicates may be connected by using logical connectives: ∧ (AND), ∨ (OR), ¬ (NOT), and ⇒ (if-then).

Tuple Relational Calculus

• Finding tuples for which a predicate is true.
• Example:

“Find the set of all tuples S such that F ( S ) is true”

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{ S | F ( S ) }

Tuple Relational Calc.

• Tuple variables on the left side of the bar “|” are called free variables.
• Tuple variables on the right side of the bar “|” must be bound variables, qualified by ∀ or ∃.

More TRC Examples

• List the names of staff who do not manage any properties. (Two ways)

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{S.fName, S.lName | Staff(S) ∧ (¬ ( ∃ P) (PropertyForRent(P) ∧ (S.StaffNo = P.StaffNo)))}

{S.fName, S.lName | Staff(S) ∧ (( ∀ P) (¬PropertyForRent(P) ∨ ¬(S.StaffNo = P.StaffNo)))}

Domain Relational Calculus

• In DRC, variables take their values from domains of attributes rather than tuples of relations.
• Somewhat similar to Π in Relational Algebra.

{d 1 , d 2 ,…,dn | F (d 1 ,d 2 ,…,dm)}, m ≥ n

Scope in DRC

• Important to restrict the scope of your variables, since they are all initially free.
• Ways of restricting your scope:

(a, b) ∈ R , variable a and b belong to relation R.

Using a Scope

• Example: Staff(name, age, rank) Family(name, age, relation)

{ name | (name = “Mike”) },

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This will look in both Staff and Family relations.

{name | name ∈ Staff ∧ name = “Mike” } Looks in only Staff