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Relational Calculus

Relational Calculus. Logic Calculus. Logic ( 논리학 ) Propositional Calculus ( 명제계산 ), Predicate Calculus ( 술어계산 ) Propositional calculus proposition( 명제 ) can be classified as true or false Syllogism ( 삼단논법 ) If Socrates is a human, Socrates will die. (p->q) Socrates is a human. (p)

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Relational Calculus

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  1. Relational Calculus

  2. Logic Calculus • Logic (논리학) Propositional Calculus (명제계산),Predicate Calculus (술어계산) • Propositional calculus proposition(명제) can be classified as true or false Syllogism (삼단논법) If Socrates is a human, Socrates will die. (p->q) Socrates is a human. (p) Socrates will die. ( (p->q)∧p) -> q 데이터베이스시스템

  3. Syllogism (삼단논법) Truth table(진리표) • Predicate Calculus propositional calculus + quantifiers such as EXISTS, FORALL 데이터베이스시스템

  4. Predicate Calculus • 예 : 모든 사람은 죽는다.Socratest는 사람이다.따라서, Socrates는 죽는다.propositional calculus로는 증명할 수 없다. • 증명 H(x) : x는 사람이다. M(x) : x는 죽는다. • ( x) (H(x) –> M(x)) • H(s) • H(s) –> M(s) by 1) & 2) Universal Instantiation • M(s) by 2) & 3) propositional logic 데이터베이스시스템

  5. Relational Algebra vs. Relational Calculus • Algebra operators are applied to relations in a specified order (procedural) • Calculus select all the tuples which make the specified condition true (non-procedural) tuple calculus vs. domain calculus 데이터베이스시스템

  6. Relational Calculus • Tuple variable a variable which represents a tuple of a relation x  학생(학번, 이름, 학년, 학과) y  과목(과목번호, 과목이름, 학점수, 학과, 담당교수) z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) • Examples • List all the student names.x  학생, { x.이름 } • List the student_numbers of students who take ‘C413’ z  수강, { z.학번 | z.과목번호= ‘C413’ } 데이터베이스시스템

  7. 집합 표시 데이터베이스시스템

  8. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점수, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) • List the names and the departments of students who are not in ‘컴퓨터’departmentx  학생, { (x.이름, x.학과) | x.학과<> ‘컴퓨터’} • List the student_number and class_numberpairs such that indicated student got higher than or equal to 90 in either the midterm or the final of the indicated classz  수강, { (z.학번, z.과목번호) | z.중간성적>= 90 or z.기말성적>= 90 } 데이터베이스시스템

  9. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) • List the student_numbers of students who got ‘A’ in the class ‘C413’z  수강, { z.학번 | z.과목번호= ‘C413’ and z.학점= ‘A’ } • List the names and departments of students who take ‘C413’ x  학생, z  수강, { (x.이름, x.학과) | EXISTS z (z.학번=x.학번 and z.과목번호= ‘C413’) } join  In  EXISTS 데이터베이스시스템

  10. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) • Find the student name which comes first in the alphabetical order. x1, x2  학생, { x1.이름| FORALL x2 (x1.이름 <= x2.이름) } • Quantifiers (정량자) EXISTS V(p) (existential quantifier, 존재정량자) : There exists at least one value V that makes p true. FORALL V(p) (univeral quantifier, 범용정량자) : For all values of V, p evaluates true. 데이터베이스시스템

  11. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) • List the student_numbersand the names of students who do not take ‘C413’. x  학생, z  수강, { (x.학번, x.이름)| NOT EXISTS z (z.학번=x.학번 and z.과목번호= ‘C413’ )}Difference  Not In  Not EXISTS • List the names of students who take at least one class from ‘컴퓨터’departmentx  학생, y 과목, z  수강, { x.이름| EXISTS z (z.학번=x.학번 and EXISTS y (y.과목번호 = z.과목번호 and y.학과= ‘컴퓨터’) ) } 데이터베이스시스템

  12. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) • List the names of students who take at least one class together with the student of student_number 100. x  학생, z1  수강, z2  수강, { x.이름| EXISTS z1 (z1.학번=x.학번 and EXISTS z2 (z2.과목번호= z1.과목번호 and z2.학번= 100 ) ) } • List the names of students who take all the listed classes in 과목 relation Algebra : ( 수강[학번, 과목번호] / 과목[과목번호] )Join 학생 ) [이름]Calculusx  학생, y 과목, z  수강, { x.이름| FORALL y (EXISTS z ( z.과목번호= y.과목번호 and z.학번=x.학번) )} 데이터베이스시스템

  13. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) ( 수강[학번, 과목번호] / 과목[과목번호] ) join 학생 ) [이름] x  학생, y 과목, z  수강, { x.이름| FORALL y (EXISTS z ( z.과목번호= y.과목번호 and z.학번=x.학번} FORALL V(p)  NOT EXISTS V(Not p) { x.이름| Not EXISTS y (Not EXISTS z ( z.과목번호= y.과목번호 and z.학번=x.학번} Denominator is the relation for the first NOT EXISTS. 데이터베이스시스템

  14. Relational Calculusx  학생 (학번, 이름, 학년, 학과)y  과목(과목번호, 과목이름, 학점, 학과, 담당교수)z  수강(학번, 과목번호, 성적, 중간성적, 기말성적) FORALL V(p)  NOT EXISTS V(Not p) All dogs are animals  There are no dogs which are not animals takes all the subjects  There are no subjects which are not taken Names of students  Names of students who take such that all the subjects there are no subjects not taken by each of them. 데이터베이스시스템

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