1 / 27

CSCE 580 Artificial Intelligence Ch.12 [P]: Individuals and Relations Datalog

CSCE 580 Artificial Intelligence Ch.12 [P]: Individuals and Relations Datalog. Fall 2009 Marco Valtorta mgv@cse.sc.edu. Acknowledgment. The slides are based on [AIMA] and other sources, including other fine textbooks

ceri
Download Presentation

CSCE 580 Artificial Intelligence Ch.12 [P]: Individuals and Relations Datalog

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSCE 580Artificial IntelligenceCh.12 [P]: Individuals and RelationsDatalog Fall 2009 Marco Valtorta mgv@cse.sc.edu

  2. Acknowledgment • The slides are based on [AIMA] and other sources, including other fine textbooks • David Poole, Alan Mackworth, and Randy Goebel. Computational Intelligence: A Logical Approach. Oxford, 1998 • A second edition (by Poole and Mackworth) is under development. Dr. Poole allowed us to use a draft of it in this course • Ivan Bratko. Prolog Programming for Artificial Intelligence, Third Edition. Addison-Wesley, 2001 • The fourth edition is under development • George F. Luger. Artificial Intelligence: Structures and Strategies for Complex Problem Solving, Sixth Edition. Addison-Welsey, 2009

  3. Databases and Recursion • Datalog is a subset of Prolog that can be used to define relational algebra • Datalog is more powerful than relational algebra: • It has variables • It allows recursive definitions of relations • Therefore, e.g., datalog allows the definition of the transitive closure of a relation. • Datalog has no function symbols: it is a subset of definite clause logic.

  4. Relational DB Operations • A relational db is a kb of ground facts • datalog rules can define relational algebra database operations • The examples refer to the database in course.pl

  5. Selection • Selection: • cs_course(X) <- department(X, comp_science). • math_course(X) <- department(X, math).

  6. Union • Union: multiple rules with the same head • cs_or_math_course(X) <- cs_course(X). • cs_or_math_course(X) <- math_course(X). • In the example, the cs_or_math_course relation is the union of the two relations defined by the rules above.

  7. Join • Join: the join is on the shared variables, e.g.: • ?enrolled(S,C) & department(C,D). • One must find instances of the relations such that the values assigned to the same variables unify • in a DB, unification simply means that the same variables have the same value!

  8. Projection • When there are variables in the body of a clause that don’t appear in the head, you say that the relation is projected onto the variables in the head, e.g.: • in_dept(S,D) <- enrolled(S,C) & department(C,D). • In the example, the relation in_dept is the projection of the join of the enrolled and department relations.

  9. Databases and Recursion • Datalog can be used to define relational algebra • Datalog is more powerful than relational algebra: • It has variables • It allows recursive definitions of relations • Therefore, e.g., datalog allows the definition of the transitive closure of a relation. • Datalog has no function symbols: it is a subset of definite clause logic.

  10. Relational DB Operations • A relational db is a kb of ground facts • datalog rules can define relational algebra database operations • The examples refer to the database in course.pl

  11. Selection • Selection: • cs_course(X) <- department(X, comp_science). • math_course(X) <- department(X, math).

  12. Union • Union: multiple rules with the same head • cs_or_math_course(X) <- cs_course(X). • cs_or_math_course(X) <- math_course(X). • In the example, the cs_or_math_course relation is the union of the two relations defined by the rules above.

  13. Join • Join: the join is on the shared variables, e.g.: • ?enrolled(S,C) & department(C,D). • One must find instances of the relations such that the values assigned to the same variables unify • in a DB, unification simply means that the same variables have the same value!

  14. Projection • When there are variables in the body of a clause that don’t appear in the head, you say that the relation is projected onto the variables in the head, e.g.: • in_dept(S,D) <- enrolled(S,C) & department(C,D). • In the example, the relation in_dept is the projection of the join of the enrolled and department relations.

  15. Recursion • Define a predicate in terms of simpler instances of itself • Simpler means: easier to prove • Examples: • west in west.pl • live in elect.pl • “Recursion is a way to view mathematical induction top-down.”

  16. Well-founded Ordering • Each relation is defined in terms of instances that are lower in a well-founded ordering, a one-to-one correspondence between the relation instances and the non-negative integers. • Examples: • west: induction on the number of doors to the west---imm_west is the base case, with n=1. • live: number of steps away from the outside---live(outside) is the base case.

  17. Verification of Logic Programs • Verifiability of logic programs is the prime motivation behind using semantics! • If g is false in the intended interpretation and g is proved from the KB, • Find the clause used to prove g • If some atom in the body of the clause is false in the intended interpretation, then debug it • Else return the clause as the buggy clause instance

  18. Verifiability II • Also need to show that all cases are covered: if an instance of a predicate is true in the intended interpretation, then one of the clauses is applicable to prove the predicate. • Also need to show termination---this is in general impossible, due to semidicidability results, but it is possible in many practical situations.

  19. Limitations • No notion of complete knowledge! • Cannot conclude that something is false. • Cannot conclude something from lack of knowledge. Example: • The relation empty_course(X) with the obvious intended interpretation cannot be defined from enrolled(S,C) relation. • The Closed World Assumption (CWA) allows reasoning from lack of knowledge.

  20. Case Study: University Rules • univ.pl • DB of student records • DB of relations about the university • Rules about satisfying degree requirements.

  21. Case Study: University Rules • This is an example of representing regulatory knowledge. • (Another great example: Sergot, M.J. et al., “The British Nationality Act as a Logic Program.” CACM, 29, 5 (may 1986), 370-386.) • DB of relations about the university (univ.pl) • Rules about satisfying degree requirements (univ.pl) • Lists are used (lists.pl)

  22. Some facts • grade(St, Course, Mark) • dept(Dept,Fac) • We would say College, not Faculty • course(Course, Dept, Level) • core_courses(Dept,CC, MinPass) • CC is a list

  23. A Rule • satisfied_degree_requirements(St,Dept) <- covers_core_courses(St,Dept) & dept(Dept, Fac) & satisfies_faculty_req(St, Fac) & fulfilled_electives(St, Dept) & enough_units(St, Dept).

  24. More Rules • Covers_core_courses(St, Dept) <- core_courses(dept, CC, MinPass) & passed_each(CC, St, MinPass)

  25. More Rules • passed(St, C, MinPass) <- grade(St, C, Gr) & Gr >= MinPass. • A recursive rule that traverses a list. • passed_each([], S, M). • passed_each([C|R], St, MinPass) <- passed(St, C, MinPass) & passed_each(R, St, MinPass).

  26. More Rules • passed_one(CL, St, MinPass) <- member(C, CL) & passed(St, C, MinPass).

  27. A KB about rooms (Fig.12.2[P])

More Related