1 / 63

Integrity constraints & constraint logic programming

Integrity constraints & constraint logic programming. Henning Christiansen Roskilde University, Denmark henning@ruc.dk INAP’99, Invited DDLP’99 talk. Constraint logic programming (CLP). 1980'ies: Built-in constraint solvers, e.g., CLP(R) 1990'ies: Constraint solving as programming paradigm,

jadyn
Télécharger la présentation

Integrity constraints & constraint logic programming

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. Integrity constraints&constraint logic programming Henning Christiansen Roskilde University, Denmark henning@ruc.dk INAP’99, Invited DDLP’99 talk

  2. Constraint logic programming (CLP) • 1980'ies: Built-in constraint solvers, e.g., CLP(R) • 1990'ies: Constraint solving as programming paradigm, • language support, e.g., Constraint Handling Rules (CHR) • 2000'ies: Efficient (WAM-like) impl's of CHR and • similar programming languages • CLP expands to more and more applications • This talk: Applying CLP for evaluation of integrity constraints

  3. Motivation • Names of phenomena overlap: • Integrity constraint/constraint logic programming

  4. Motivation • Names of phenomena overlap: • Integrity constraint/constraint logic programming • IC's: Knowledge about database for improved query-answering: • – controlling update request • – intentional answers • – semantic query optimization • – usually avioded, approximated by update routines/simple checks

  5. Motivation • Names of phenomena overlap: • Integrity constraint/constraint logic programming • IC's: Knowledge about database for improved query-answering: • – controlling update request • – intentional answers • – semantic query optimization • – usually avioded, approximated by update routines/simple checks • CLP: A declarative, computational paradigm • – delay’s • – incrementality: self-simplifying, self-specializing code • – produces general (quantified) answers Relevant for ICs!

  6. The idea: Lazy negation-as-failure • Restrict to positive DDB's (with ”=” and ”dif”), and IC's as ”denials”: • bottom :- father(A,_), mother(A,_) • bottom:- father(A,C), father(B,C), dif(A,B) • tested by negation-as-failure that bottom is not the case.

  7. The idea: Lazy negation-as-failure • Restrict to positive DDB's (with ”=” and ”dif”), and IC's as ”denials”: • bottom :- father(A,_), mother(A,_) • bottom:- father(A,C), father(B,C), dif(A,B) • tested by negation-as-failure that bottom is not the case. • Lazyness?? • A prospective update => a (constrained) ”hole” in the database • Procedure delays when ”hole” is met • Resulting computation: • – known part of DB checked, specialized constr’s remain for ”holes”, • – wakes up when update arrives, checking it • – ... and mutating into new specialized constraints for future updates.

  8. The idea: Lazy negation-as-failure • Restrict to positive DDB's (with ”=” and ”dif”), and IC's as ”denials”: • bottom :- father(A,_), mother(A,_) • bottom:- father(A,C), father(B,C), dif(A,B) • tested by negation-as-failure that bottom is not the case. • Lazyness?? • A prospective update => a (constrained) ”hole” in the database • Procedure delays when ”hole” is met • Resulting computation: • – known part of DB checked, specialized constr’s remain for ”holes”, • – wakes up when update arrives, checking it • – ... and mutating into new specialized constraints for future updates. • I.e. Incrementality!

  9. A meta-logic approach to lazy negation-as-failure • Ground representation of object language, e.g.: • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ]

  10. A meta-logic approach to lazy negation-as-failure • Ground representation of object language, e.g.: • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Instance constraints: • instance(s,t) iff s, t name object S, T with T an instance of S • Example: instance(p('X'), p(a))

  11. Instance constraints reflect object var’s to Prolog • Example: • instance(p('X'), Z) <==> Z = p(ZX) • Object unification = 2*instance + 1 Prolog unification

  12. Instance constraints reflect object var’s to Prolog • Example: • instance(p('X'), Z) <==> Z = p(ZX) • Object unification = 2*instance + 1 Prolog unification • Example: • Object level: p(a,X) = p(Y,b) • Meta-level (= Prolog): • instance(p(a,'X'), Z1), instance(p('Y',b), Z2), Z1=Z2 • Z1 = p(a, ZX), Z2 = p(ZY,b), Z1=Z2 • ZX=b, XY=a • Thus: Semantic prop’s of ground repr. with efficiency of nonground repr.

  13. Solving instance constraints... (sketch) • Straight-forward recursive decomposition, delay’s when first argument is a variable • Interacts with user constraint • constant(X) iff ”X names an object constant” • Examples: • instance(p('X'), Z) <==> Z = p(ZX) • instance(p(X), Z) <==> Z = p(ZX), instance(X,ZX) • instance(p(X),Z), constant(X) <==> constant(X), Z = p(X) • I.e. meta-var’s covered by constant take ”active” part in computation

  14. Lazy negation-as-failure (top-level procedure) • Declaratively: • fails(p,q) iff p, q names of P, Q where Q fails in P, • i.e. no  with P |– Q  • Top-level of implementation: • fails(P,Q):- instance(Q,Q1), fails1(P,Q1). • where fails1(p,q1) iff p, q names of P, Q1 where not P |– Q1 • fails1/2 implemented by constraint solver and auxiliary constraints.

  15. Lazy negation-as-failure (top-level procedure) • Declaratively: • fails(p,q) iff p, q names of P, Q where Q fails in P, • i.e. no  with P |– Q  • Top-level of implementation: • fails(P,Q):- instance(Q,Q1), fails1(P,Q1). • where fails1(p,q1) iff p, q names of P, Q1 where not P |– Q1 • fails1/2 implemented by constraint solver and auxiliary constraints. • ... but let’s see some examples first

  16. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ]

  17. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:fails(DB0, bottom)

  18. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:fails(DB0, bottom) • A:yes

  19. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:fails(DB0& [Clause], bottom)

  20. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:fails(DB0& [Clause], bottom) • A: ... a complicated expression ready for all possibilities: • Clause could be a father clause, • a mother clause, • or a new IC, i.e, bottom:- ...

  21. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:constant(A), constant(B), • fails(DB0 & [(father(A,B):- true)],bottom)

  22. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:constant(A), constant(B), • fails(DB0 & [(father(A,B):- true)],bottom) • A:fails1(jane=A),fails1((mary=B, dif(john,A)))

  23. IC’s evaluated by lazy negation-as-failure (examples) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:constant(A), constant(B), no_duplicates( ... ), • fails(DB0 & [(father(A,B):- true)],bottom) • A:fails1(jane=A), fails1(mary=B)

  24. Observations (preliminary) • Constraint solver produces residual constraints similar to "simplification method" [Nicolas, 82; Sadri,Kowalski, 88], but here as by-product of checking the whole, parameterized database • A flavour of constructive negation (later example: instantiates variables)

  25. Incrementality for sequences of updates • A new user constraint (example): • clause_pattern(F,(father(X,Y):-true),(constant(X),constant(Y))) • iff all clauses in F obey pattern and constraints • A new residual constraint: • fails1(Prog,Atom*Clause(s),Continue) • iff • for (each) instance of clause H:-B in Clause(s), • the query H=Atom,B,Continue fails in Prog.

  26. Incrementality for sequences of updates (example) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:clause_pattern(F,(father(X,Y):-true),(constant(X),constant(Y))), • fails1(DB0 & F, bottom), no_duplicates(...)

  27. Incrementality for sequences of updates (example) • DB0 = • [(bottom:- dif('A','B'), father('A','C'), father('B','C')), • (bottom:- dif('A','B'), mother('A','C'), mother('B','C')), • (bottom:- father('A','Z'), mother('A','X')), • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:clause_pattern(F,(father(X,Y):-true),(constant(X),constant(Y))), • fails1(DB0 & F, bottom), no_duplicates(...) • A:fails1(DB0 & F,father(A1,Z1)*F,mother(A1,X1)), • fails1(DB0 & F,father(B2,mary)*F, dif(john,B2)), • fails1(DB0 & F,(father(A3,C3),father(B3,C3))*F, dif(A3,B3)) • NB: Optimization for symmetric literals applied

  28. View update, lazy N-a-F co-operates with abduction • A constraint-based proof predicate for program synthesis: • demo(p,q) iff p, q names of P, Q where Q succeds in P

  29. View update, lazy N-a-F co-operates with abduction • A constraint-based proof predicate for program synthesis: • demo(p,q) iff p, q names of P, Q where Q succeds in P • DB1 = [(bottom:- ....), ..., • (sibling('A','B'):- ....), ..., • (father(john,mary):- true), • (mother(jane,mary):- true) ]

  30. View update, lazy N-a-F co-operates with abduction • A constraint-based proof predicate for program synthesis: • demo(p,q) iff p, q names of P, Q where Q succeds in P • DB1 = [(bottom:- ....), ..., • (sibling('A','B'):- ....), ..., • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:clause_pattern(F, (father...), ...), • clause_pattern(M, (mother...), ...), • fails1(DB1 & F & M, bottom), no_duplicates(...) • demo(DB1 & F & M, sibling(bob,mary)).

  31. View update, lazy N-a-F co-operates with abduction • A constraint-based proof predicate for program synthesis: • demo(p,q) iff p, q names of P, Q where Q succeds in P • DB1 = [(bottom:- ....), ..., • (sibling('A','B'):- ....), ..., • (father(john,mary):- true), • (mother(jane,mary):- true) ] • Q:clause_pattern(F, (father...), ...), • clause_pattern(M, (mother...), ...), • fails1(DB1 & F & M, bottom), no_duplicates(...) • demo(DB1 & F & M, sibling(bob,mary)). • A:F = [(father(john,bob):-true) | F1], or • M = [(mother(jane,bob):-true) | F1]

  32. ”Co-operative” human-machine dialogue (example) • U: Isn’t aunt Dora the mother of Mary? Let's ask... • Q:demo(DB0, mother(dora,mary)) • A:no

  33. ”Co-operative” human-machine dialogue (example) • U: Isn’t aunt Dora the mother of Mary? Let's ask... • Q:demo(DB0, mother(dora,mary)) • A:no • U: !?!?Hmmmm, perhaps they forgot to add it to the database? • Q:fails(DB0 & [(mother(dora,mary):-true)], bottom)

  34. ”Co-operative” human-machine dialogue (example) • U: Isn’t aunt Dora the mother of Mary? Let's ask... • Q:demo(DB0, mother(dora,mary)) • A:no • U: !?!?Hmmmm, perhaps they forgot to add it to the database? • Q:fails(DB0 & [(mother(dora,mary):-true)], bottom) • A:no • U: ... but why? I'm confused ... do you have a mother for Mary? • Q:constant(A), demo(DB0, mother(A, mary))

  35. ”Co-operative” human-machine dialogue (example) • U: Isn’t aunt Dora the mother of Mary? Let's ask... • Q:demo(DB0, mother(dora,mary)) • A:no • U: !?!?Hmmmm, perhaps they forgot to add it to the database? • Q:fails(DB0 & [(mother(dora,mary):-true)], bottom) • A:no • U: ... but why? I'm confused ... do you have a mother for Mary? • Q:constant(A), demo(DB0, mother(A, mary)) • A:A = jane(no more answers)

  36. ”Co-operative” human-machine dialogue (example) • U: Isn’t aunt Dora the mother of Mary? Let's ask... • Q:demo(DB0, mother(dora,mary)) • A:no • U: !?!?Hmmmm, perhaps they forgot to add it to the database? • Q:fails(DB0 & [(mother(dora,mary):-true)], bottom) • A:no • U: ... but why? I'm confused ... do you have a mother for Mary? • Q:constant(A), demo(DB0, mother(A, mary)) • A:A = jane(no more answers) • U: So Jane is the only known mother, but why can't we add aunt Dora? • Q:constant(A), fails(DB0 & [(mother(A,mary):- true)], bottom)

  37. ”Co-operative” human-machine dialogue (example) • U: Isn’t aunt Dora the mother of Mary? Let's ask... • Q:demo(DB0, mother(dora,mary)) • A:no • U: !?!?Hmmmm, perhaps they forgot to add it to the database? • Q:fails(DB0 & [(mother(dora,mary):-true)], bottom) • A:no • U: ... but why? I'm confused ... do you have a mother for Mary? • Q:constant(A), demo(DB0, mother(A, mary)) • A:A = jane(no more answers) • U: So Jane is the only known mother, but why can't we add aunt Dora? • Q:constant(A), fails(DB0 & [(mother(A,mary):- true)], bottom) • A:A = jane(no more answers) • U: ... so Jane is the only possible mother...

  38. Observations (continued) • Constraint solver produces residual constraints similar to "simplification method" [Nicolas, 82; Sadri, Kowalski, 88], but here as by-product of checking the whole, parameterized database • A flavour of constructive negation

  39. Observations (continued) • Constraint solver produces residual constraints similar to "simplification method" [Nicolas, 82; Sadri, Kowalski, 88], but here as by-product of checking the whole, parameterized database • A flavour of constructive negation • Implies an incremental evaluation of IC’s: for each update, evaluate it, and prepare for next update

  40. Observations (continued) • Constraint solver produces residual constraints similar to "simplification method" [Nicolas, 82; Sadri, Kowalski, 88], but here as by-product of checking the whole, parameterized database • A flavour of constructive negation • Implies an incremental evaluation of IC’s: for each update, evaluate it, and prepare for next update • Use of constraints provides optimal interleaving with abductive procedure for free for view update(opp. algorithms [Decker, Kowalski & al, Denecker & al, ...] with explicit scheduling)

  41. Observations (continued) • Constraint solver produces residual constraints similar to "simplification method" [Nicolas, 82; Sadri, Kowalski, 88], but here as by-product of checking the whole, parameterized database • A flavour of constructive negation • Implies an incremental evaluation of IC’s: for each update, evaluate it, and prepare for next update • Use of constraints provides optimal interleaving with abductive procedure for free for view update(opp. algorithms [Decker, Kowalski & al, Denecker & al, ...] with explicit scheduling) • IC’s used to produce useful answers in human-machine dialogue (though not giving ”arguments”)

  42. Observations (continued) • Constraint solver produces residual constraints similar to "simplification method" [Nicolas, 82; Sadri, Kowalski, 88], but here as by-product of checking the whole, parameterized database • A flavour of constructive negation • Implies an incremental evaluation of IC’s: for each update, evaluate it, and prepare for next update • Use of constraints provides optimal interleaving with abductive procedure for free for view update(opp. algorithms [Decker, Kowalski & al, Denecker & al, ...] with explicit scheduling) • IC’s used to produce useful answers in human-machine dialogue (though not giving ”arguments”) • ... now, let’s have a look at that constraint solver

  43. Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  44. fails1(_,true) <=> fail Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  45. fails1(_,true) <=> fail fails1(P, (Q1,(A=B),Q2)) <=> (A=B -> fails1(P,(Q1,Q2));true) Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  46. fails1(_,true) <=> fail fails1(P, (Q1,(A=B),Q2)) <=> (A=B -> fails1(P,(Q1,Q2));true) fails1(P, (Q1,dif(A,B),Q2)) <=> A==Bor both are constants or one is a variable free in(Q1,Q2) | (A==B -> true;fails1(P,(Q1,Q2))) Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  47. fails1(_,true) <=> fail fails1(P, (Q1,(A=B),Q2)) <=> (A=B -> fails1(P,(Q1,Q2));true) fails1(P, (Q1,dif(A,B),Q2)) <=> A==Bor both are constants or one is a variable free in(Q1,Q2) | (A==B -> true;fails1(P,(Q1,Q2))) fails1(P, (Q1, A, Q2)) <=> A names an atom | fails1(P, A*P, (Q1,Q2)) Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  48. fails1(_,true) <=> fail fails1(P, (Q1,(A=B),Q2)) <=> (A=B -> fails1(P,(Q1,Q2));true) fails1(P, (Q1,dif(A,B),Q2)) <=> A==Bor both are constants or one is a variable free in(Q1,Q2) | (A==B -> true;fails1(P,(Q1,Q2))) fails1(P, (Q1, A, Q2)) <=> A names an atom | fails1(P, A*P, (Q1,Q2)) fails1(_, _*[], _) <=> true Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  49. fails1(_,true) <=> fail fails1(P, (Q1,(A=B),Q2)) <=> (A=B -> fails1(P,(Q1,Q2));true) fails1(P, (Q1,dif(A,B),Q2)) <=> A==Bor both are constants or one is a variable free in(Q1,Q2) | (A==B -> true;fails1(P,(Q1,Q2))) fails1(P, (Q1, A, Q2)) <=> A names an atom | fails1(P, A*P, (Q1,Q2)) fails1(_, _*[], _) <=> true fails1(P, A*[C|Cs], Cont) <=> fails1(P, A*C, Cont), fails1(P, A*Cs, Cont) Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

  50. fails1(_,true) <=> fail fails1(P, (Q1,(A=B),Q2)) <=> (A=B -> fails1(P,(Q1,Q2));true) fails1(P, (Q1,dif(A,B),Q2)) <=> A==Bor both are constants or one is a variable free in(Q1,Q2) | (A==B -> true;fails1(P,(Q1,Q2))) fails1(P, (Q1, A, Q2)) <=> A names an atom | fails1(P, A*P, (Q1,Q2)) fails1(_, _*[], _) <=> true fails1(P, A*[C|Cs], Cont) <=> fails1(P, A*C, Cont), fails1(P, A*Cs, Cont) fails1(P,A*(H:-B), Cont) <=> copy_term((A,Cont),(A1,Cont1)), instance((H:-B),(H1,B1)), fails1(P,(H1=A1,B1, Cont1)) Constraint solver for lazy negation-as-failure– Simplified CHR’s; first version for known program and query

More Related