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Introduction to Datalog: Database Logic and Predicate Arguments in Query Languages

This document provides an overview of Datalog, a logical query language used in database systems. It covers the structure of relational atoms, their arguments, and the Boolean values they can take. The paper discusses Datalog rules, emphasizing the importance of safety conditions to prevent underspecified queries. Various examples illustrate the implementation of Datalog, including both extensional and intensional predicates. Key aspects of bag semantics are also examined, showcasing how duplicates can be treated in query results.

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Introduction to Datalog: Database Logic and Predicate Arguments in Query Languages

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  1. ICS 321 Fall2011Algebraic and Logical Query Languages (ii) Asst. Prof. Lipyeow Lim Information & Computer Science Department University of Hawaii at Manoa Lipyeow Lim -- University of Hawaii at Manoa

  2. Datalog : Database Logic Predicate Arguments • A (relational) atom • Consists of a predicate and a list of arguments • Arguments can be constants or variables • Takes on Boolean value (true or false) • A relation R can be represented as a predicate R • A tuple <a,b,c,d,e,f,g> is in R iff the atom R(a,b,c,d,e,f,g) is true. R(a,b,c,d,e,f,g) Atom Lipyeow Lim -- University of Hawaii at Manoa

  3. Example: tables in datalog R Datalog R(1,2) R(3,4) True by default. R(1,4) would be false Lipyeow Lim -- University of Hawaii at Manoa

  4. Arithmetic Atoms x < y x+1 >= y+4*z Can contain both constants and variables. Lipyeow Lim -- University of Hawaii at Manoa

  5. Datalog Rules Shorthand for AND “if” or  head body LongMovie(t,y) :- Movies(t,y,l,g,s,p) , l >=100 (t,y) is a tuple of LongMovieIF (t,y,l,g,s,p) is a tuple of Movies and length of movie is at least 100 Aka “subgoal” Can be preceded by negation operator “NOT” or “~” These two “t,y” have to match These two “l” have to match Anonymous variables LongMovie(t,y) :- Movies(t,y,l,_,_,_) , l >=100 Lipyeow Lim -- University of Hawaii at Manoa

  6. Safety Condition for Datalog Rules Every variable that appears anywhere in the rule must appear in some nonnegated, relational subgoalof the body • Without the safety condition, rules may be underspecified, resulting in an infinite relation (not allowed). • Examples • LongMovie(t,y) :- Movies(t,y,l,_,_,_) , l >=100 • P(x,y) :- Q(x,z), NOT R(w,x,z), x<y Lipyeow Lim -- University of Hawaii at Manoa

  7. Alternative Interpretation: Consistency Datalog Q(1,2) Q(1,3) R(2,3) R(3,1) P(x,y) :- Q(x,z), R(z,y), NOT Q(x,y) • For each consistent assignment of nonnegated, relational subgoal, • Check the negated, relational subgoals and the arithmetic subgoals for consistency Yes false No, z=2,3 No, z=2,3 Yes P(1,1) true Lipyeow Lim -- University of Hawaii at Manoa

  8. Intensionalvs Extensional Datalog • Extensional predicates – relations stored in a database • Intensional predicates – computed by applying one or more datalog rules Q(1,2) Q(1,3) R(2,3) R(3,1) P(x,y) :- Q(x,z), R(z,y), NOT Q(x,y) extensional intensional Lipyeow Lim -- University of Hawaii at Manoa

  9. What about bag semantics ? • Datalog still works if there are no negated, relational subgoals. • Treat duplicates like non-duplicates Datalog R(1,2) R(1,2) S(2,3) S(4,5) S(4,5) H(x,z) :- R(x,y), S(y,z) Yes H(1,3) No, y=2,4 No, y=2,4 Lipyeow Lim -- University of Hawaii at Manoa

  10. Example 1 Datalog Answer(x,y) :- A(x,y) Answer(x,y) :- B(x,y) Lipyeow Lim -- University of Hawaii at Manoa

  11. Example 2 Datalog Answer(x,y) :- A(x,y), B(x,y) Lipyeow Lim -- University of Hawaii at Manoa

  12. Example 3 Datalog Answer(x,y) :- A(x,y), NOT B(x,y) Lipyeow Lim -- University of Hawaii at Manoa

  13. Example 4 Datalog Answer(x,y) :- A(x,y), x > 10, y = 200 Lipyeow Lim -- University of Hawaii at Manoa

  14. Example 5 Datalog Answer(x) :- A(x,y) Lipyeow Lim -- University of Hawaii at Manoa

  15. Example 6 Datalog Answer(w,x,y,z) :- A(w,x), B(y,z) Lipyeow Lim -- University of Hawaii at Manoa

  16. Example 7 Datalog Answer(w,x,y) :- A(w,x), B(x,y) Lipyeow Lim -- University of Hawaii at Manoa

  17. Example 8 Datalog Answer(w,x,z) :- A(w,x), B(y,z), x>y Lipyeow Lim -- University of Hawaii at Manoa

  18. Example 9 Datalog Path(x,y) :- Edge(x,y) Path(x,z) :- Edge(x,y), Edge(y,z) Lipyeow Lim -- University of Hawaii at Manoa

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