L05 - queries and tuple calculus

L05 - queries and tuple calculus - Recall from last time...

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Unformatted text preview: Recall from last time: Recall from last time: Queries expressed using first order logic Queries expressed using first order logic ¡ The example scenario: ¢ Student(name, college, major, gpa) ¢ Faculty(name, dept, salary, year_hired) ¢ Chair(dept, name) ¢ Teaches(name, course) ¢ Enrolls(name, course) ¡ List the names of faculty that have the highest salary in their department ¢ ∃ (d, s, y) (Faculty(n, d, s, y) ∧ ∀ (n1, s1, y1) (Faculty(n1, d, s1, y1) → (s ≥ s1))) or we could say ¢ ∃ (d, s, y)( Faculty(n, d, s, y) ∧ ¬ ( ∃ n1, s1, y1) (Faculty(n1, d, s1, y1) ∧ (s < s1))) Remember: P → Q ⇔ ¬ P ∨ Q DeMorgan’s Law: ¬ (A ∨ B) ⇔ ( ¬ A ) ∧ ( ¬ B ) Queries in Domain Relational Calculus in text Queries in Domain Relational Calculus in text notation notation ¡ Each query is an expression of the form: { < x 1 , x 2 , …, x n > | P ( x 1 , x 2 , …, x n )} ¢ x 1 , x 2 , …, x n represent domain variables ¢ P represents a formula similar to that of the predicate calculus ¡ Text example schema: ¢ branch ( branch_name, branch_city, assets ) ¢ customer ( customer_name, customer_street, customer_city ) ¢ account ( account_number, branch_name, balance ) ¢ loan ( loan_number, branch_name, amount ) ¢ depositor ( customer_name, account_number ) ¢ borrower ( customer_name, loan_number ) And an example query in text notation: And an example query in text notation: ¡ Find the names of all customers having a loan, an account, or both at the Perryridge branch: { < c > | ∃ l ( < c, l > ∈ borrower ∧ ∃ b,a ( < l, b, a > ∈ loan ∧ b = “Perryridge” ) ) ∨ ∃ a ( < c, a > ∈ depositor ∧ ∃ b,n ( < a, b, n > ∈ account ∧ b = “Perryridge” ) ) } ¡ Notice the form of the query: { < x 1 , x 2 , …, x n > | P ( x 1 , x 2 , …, x n )} ¡ x 1 , x 2 , …, x n represent domain variables ¡ P represents a formula similar to that of the predicate calculus ¡ Notice that in all of the DRC queries, we had to pay attention to the order of the columns as we framed the query. ¢ we had to remember, for example, that the first column of the loan relation is the loan_number, the second the branch_name, the third the amount ¢ that means that we effectively need to keep the details of the relation schema in our heads all the time – down to the order of the columns ¢ this is a pain!...
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L05 - queries and tuple calculus - Recall from last time...

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