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Datalog: Logic Instead of Algebra

Datalog is a logic-based programming language that uses if-then rules to mimic relational algebra operators, providing a powerful framework for database queries. Unlike relational algebra, Datalog can express recursive queries through its rules, making it a more expressive and flexible option for data manipulation. Relations in Datalog are represented as predicates with their arguments termed atoms. Datalog distinguishes between extensional predicates (stored in databases) and intentional predicates (derived from rules). This approach enhances query capabilities, allowing complex operations to be performed intuitively.

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Datalog: Logic Instead of Algebra

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  1. Datalog: Logic Instead of Algebra

  2. Datalog: Logic instead of Algebra • Each relational-algebra operator can be mimicked by one or several Database Logic (Datalog) that consists of if-then rules. Datalog is inherently a logic of sets • Datalog queries are more powerful than relational algebra; several rules can express recursions that are not expressable in algebra • Relations are represented in Datalog as predicates; predicate (R) is followed by its arguments is called an atom • Predicate returns a boolean value

  3. Datalog: Logic instead of Algebra • Rule: head  body • Head: relational atom • : read “if” • Body: one or more atoms called subgoals which may be relational or arithmetic • Example: LongMovie(t,y)  Movies(t,y,l,s,p) AND l ≥ 100 • It says: LongMovie(t,y) is true whenever we can find tuple in Movies with: first 2 components as (t,y) and 3rd component as l that is at least 100, and any values in components 4 and 5 • Equivalent to assignment statement in relational algebra: LongMovie := ∏title,year (σlength≥100(Movies))

  4. Datalog: Logic instead of Algebra • Extensional and Intentional Predicates: • Extensional Predicates (EDB) are predicates whose relations are stored in a database • Intentional Predicates (IDB) are predicates whose relations are computed by applying one or more Datalog rules • As long as there is no negated relational subgoals, evaluating rules when relations are sets apply for bags as well • Relational Algebra and Datalog: assume R(A,B,C), and S(A,B,C): • Boolean: • Union: R υ S is equivalent to these 2 rules: • U(A,B,C)  R(A,B,C) • U(A,B,C)  S(A,B,C)

  5. Datalog: Logic instead of Algebra • Intersection: R ∩ S is equivalent to the following rule: • I(A,B,C)  R(A,B,C) AND S(A,B,C) • Set Difference: R - S is equivalent to the following rule: • D(A,B,C)  R(A,B,C) AND NOT S(A,B,C) • Projection • P(A,B)  R(A,B,C) • Selection • S(A,B,C)  R(A,B,C) AND C ≥ 100 • Product • P(A,B,C,D,E.F)  R(A,B,C) AND S(D,E,F) • Joins • J(A,B,C,D)  R(A,B) AND (S(B,C,D)

  6. Datalog: Logic instead of Algebra • Simulating Multiple Operations with Datalog • Example: Algebraic Expression • ∏Title,year (σlength ≥ 100(Movies) ∩ σStudioName=‘Fox’(Movies)) • Translates into this set of rules: • W(t,y,l,g,s,p)  Movies(t,y,l,g,s,p) AND l ≥ 100 • X(t,y,l,g,s,p)  Movies(t,y,l,g,s,p) AND s = ‘Fox’ • Y(t,y,l,g,s,p)  W(t,y,l,g,s,p) AND X(t,y,l,g,s,p) • Answer(t,y)  Y(t,y,l,g,s,p)

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