Chapter08BRelationalCalculus.pptx

The formula tf is true if the formula f evaluates to

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The formula  t)(F) is true if the formula F evaluates to true for every tuple (in the universe) assigned to free occurrences of t in F; otherwise  t)(F) is false. Relational Calculus 7
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The Existential and Universal Quantifiers is called the universal or “for all” quantifier because every tuple in “the universe of” tuples must make F true to make the quantified formula true. is called the existential or “there exists” quantifier because any tuple that exists in “the universe of” tuples may make F true to make the quantified formula true. Relational Calculus 8
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Example Query Using Existential Quantifier Retrieve the name and address of all employees who work for the ‘Research’ department. The query can be expressed as : {t.FNAME, t.LNAME, t.ADDRESS | EMPLOYEE(t) and  d) (DEPARTMENT(d) and d.DNAME=‘Research’ and d.DNUMBER=t.DNO) } The only free tuple variables in a relational calculus expression should be those that appear to the left of the bar ( | ). In above query, t is the only free variable; it is then bound successively to each tuple. If a tuple satisfies the conditions specified in the query, the attributes FNAME, LNAME, and ADDRESS are retrieved for each such tuple. The conditions EMPLOYEE (t) and DEPARTMENT(d) specify the range relations for t and d. The condition d.DNAME = ‘Research’ is a selection condition and corresponds to a SELECT operation in the relational algebra, whereas the condition d.DNUMBER = t.DNO is a JOIN condition. Relational Calculus 9
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Example Query Using Existential Quantifier Find the names of employees who work on all the projects controlled by department number 5. The query can be: {e.LNAME, e.FNAME | EMPLOYEE(e) and  x)(not(PROJECT(x)) or not(x.DNUM=5) OR  w)(WORKS_ON(w) and w.ESSN=e.SSN and x.PNUMBER=w.PNO))))} Exclude from the universal quantification all tuples that we are not interested in by making the condition true for all such tuples . The first tuples to exclude (by making them evaluate automatically to true) are those that are not in the relation R of interest. In query above, using the expression not(PROJECT(x)) inside the universally quantified formula evaluates to true all tuples x that are not in the PROJECT relation. Then we exclude the tuples we are not interested in from R itself. The expression not(x.DNUM=5) evaluates to true all tuples x that are in the project relation but are not controlled by department 5. Finally, we specify a condition that must hold on all the remaining tuples in R.  w)(WORKS_ON(w) and w.ESSN=e.SSN and x.PNUMBER=w.PNO) Relational Calculus 10
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Safe Expressions Expressions using negation, the universal quantifier, and the existential quantifier must make sense An safe expression is one guaranteed to yield a finite number of tuples For example {t|NOT(employee(t))} is not safe Relational Calculus 11
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Languages Based on Tuple Relational Calculus The language SQL is based on tuple calculus. It uses the basic block structure to express the queries in tuple calculus: SELECT <list of attributes> FROM <list of relations> WHERE <conditions>
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  • Fall '09
  • SUNANHAN
  • Relational model, Quantification, Universal quantification, QBE, Domain relational calculus

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