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Propose and Revise, Truth Maintenance Systems

Propose and Revise, Truth Maintenance Systems. VT and SALT, Propose and Revise Dependency Networks and Justifications Protege: Application-independent Knowledge Acquisition. A Construction Problem: Elevator Design. Compose installation from parts

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Propose and Revise, Truth Maintenance Systems

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  1. Propose and Revise,Truth Maintenance Systems VT and SALT, Propose and Revise Dependency Networks and Justifications Protege: Application-independent Knowledge Acquisition Expert Systems 13

  2. A Construction Problem: Elevator Design Compose installation from parts • Safety Requirement:Force on cable < StrengthFire regulations • Customer Requirement:Capacity = 10 personsCan transport coffee cart • Engineering Requirement:Weight is limited by motor power and gear reductionCar width smaller than shaft width minus counterweight Expert Systems 13

  3. Designing for Elevators? • Designing requires several choices to be made:Repeated Heuristic Classification?Requirements formulated for combination • Partial solution • may show inconsistency • usually does not show feasibility • Propose-and-Apply Method: (Greedy)relies on sufficient constraint in every step, Lect 14. • Backtracking:Constraints depend on previous choices • Goal is more than configuring set of partsWork out complete installation from user requirements so problem is unpredictably constrained Expert Systems 13

  4. Start state X X X QED X QED Backtracking for Elevators? • Backtracking is useful where choices are meaningful only in context of previous ones • Example: furniture placement • No co-location • Couch opposite TV • Where constraints on steps do not (mainly) derive from earlier steps, backtracking or jumping may waste too much work Expert Systems 13

  5. PSM: Propose and Revise • Make design choices in Forward manner • When a subproblem is overconstrained1. try a fix (revision of an earlier choice)2. try a backjump (restore earlier state) • Example: • At one stage, choose elevator door type • In later stage, choose cabling system • Compute space left in shaft for car, possible door width • Find out that with this cabling system, and shaft width, door becomes too narrow: violates user constraint • Human Experts may consider to keep this cabling system, but choose another door type. Expert Systems 13

  6. 1½ SALT can find out possible fixes, but selection is based on HE knowledge Knowledge Requirements for Propose and Revise • Design parameters: • Declarative domain knowledge • How to extend a design • Procedural domain knowledge • What the constraints are • Declarative domain knowledge • What to do on violation? • Knowledge of suitable fix upon detecting a violation • Insight in suitable fix upon detecting a violation VT / SALT is at level ?? Expert Systems 13

  7. Engineering calculation:IF KNOWN pw, ow AND doortype=centerTHEN jamb = (pw – ow)/2 Try revision on violation:IF Violation of cable forceTHEN Incr nr of cables Incr cable strenght Antagonistic Constraints: Repair of one aggrevates other Traction ratio Cable force When antagonistic constraints are violated, backtrack. Example VT rules Expert Systems 13

  8. 1000rules written directly Acquisition guided through SALT 2000 rules VT Rule Base~3000 rules SALT: Knowledge Acquisition for VT • SALT knows about PSM and its knowledge requirements • Prompts user for • Design parameters • Procedures to compute values • Constraints • Revise suggestions • Checks knowledge consistency by comparing with dependency network • Compiles knowledge into rules for VT Expert Systems 13

  9. Dependency networks • Belief revision systems, truth maintenance systems • Track justifications for derived facts • Retract facts upon contradiction • Update beliefs under update of premisses • Non-monotonic networks support default reasoning • Dependency networks can be used for • Contradiction management (Elevator design) • Timed reasoning (Law enforcement) • Dynamic input (Plant monitor) • CLIPS and PROLOG maintain set of derived clauses, but (normally) without information about its derivation Expert Systems 13

  10. Nodes correspond to factsPremisses: Inputs (initial facts)Derived nodes: RHS of justification“Arcs”: justifications (rules)Use PROLOG-like notation in this lecture Status of node:in means derivedout means not derived Contradiction: Node that may not be in Fact/Rule base: b. d. c :- b, d. e :- a, c. out a e in b out c out d in Monotone dependency networks Expert Systems 13

  11. out a e in b out c in d in Labeling of dependency network • Assignment of in or out to each node • Relaxed: for each x :- y, z, if y and z are in, so is xSatisfies all logical implications expressed in rules. • Consistent: dito plus for each inx, x is a premisse or there is an x :- y, z such that y and z are in. An acyclic monotone dependency network has, for each labeling of its premisses, exactly one Relaxed, Consistent labeling Expert Systems 13

  12. a b Cyclic dependency networks • Cyclic network may have more than one consistent labeling • Example: a :- b. b :- a. • a and b can be both in, or can be both out. • The in-labeling is consistent because a is justified by b and b is justified by a… • Consistent labeling is grounded if no node contributes to its own justification:There is an ordering on in nodes s.t. each is justified only by smaller nodes A monotone dependency network has, for each labeling of its premisses, exactly one Relaxed, Consistent, Grounded labeling, which is found by Bottom Up inferencing. Top Down inferencing verifies if one given node is in. Expert Systems 13

  13. a is: opening-width >= 100(User requirement) b is: door-type = center(Most popular type) d is: car-width = 180(From shaft width) c is: opening-width <= 90(Engineering constraint) e is: Contradiction Deriving a contradiction can be traced back to our explicit premisse door-type = center a e b c d Example: Elevator door width More elegant solution: Default reasoning using non-monotone justifications Expert Systems 13

  14. Non-monotonic argumentation in crime • A person with a motive, but no alibi, is suspect • Rule Sus(X) :- Mot(X), ¬Ali(X).requires to prove absense of alibi before suspicion. • A person with a motive is suspect if we do not (yet) know him to have an alibi • Rule Sus(X) :- Mot(X) -: Ali(X).This is a non-monotonic justification • Monotone dependency network:Adding premisses can only add derivations • Non-monotonic dependency network:Adding premisses may force to retract conclusions Expert Systems 13

  15. a e b c d Non-monotonic dependency networks • a is: opening-width >= 100(User requirement) • b is: door-type = special(rare, so: initially out) • d is: car-width = 180(From shaft width) • c is: opening-width <= 90(Engineering constraint) • e is: Contradiction Expert Systems 13

  16. Assignment to non-monotone networks • Assignment of in or out to each node • Relaxed: for each x :- y, z -: u, v., if y and z are in and u and v are out, then x is inSatisfies all logical implications expressed in rules. • Consistent: dito plus for each inx, x is a premisse or there is an x :- y, z-: u, v. such that y and z are in and u and v are out. • Grounded: Consistent, Relaxed, no node contributes to its own justification:ordering on variables s.t. for each inx there is a justification with y, z earlier than x. Expert Systems 13

  17. Mot(T) Mot(S) Sus(S) Sus(T) in Ali(T) Ali(S) Mur(S) Mur(T) Wea(T) Wea(S) • Mur(X) :- Sus(X), Wea(X) -: Sus(Y). Who is convicted? Tom gets an alibi. Who is convicted? Dependency network solves murder case in • Sus(X) :- Mot(X) -: Ali(X). • Mur(X) :- Sus(X), Wea(X). Who is convicted? out out in out in Expert Systems 13

  18. a b d c Cycles in a dependency network • Even/odd: count non- monotone reasons • Even cycle: multiple consistent labelings Grounded? • Odd cycle: No consistent labeling a b d c Both consistent labelings in the even cycle are grounded because for the justification of an in node we only search back over in nodes, not over out nodes. Expert Systems 13

  19. Grounded labelings • Relaxed: each justified node is inConsistent: each in node is justifiedGrounded: no node is needed for its own justification • Grounded labelings provide simple explanations for all deduced phenomena. • Monotone networks have one grounded labeling • Acyclic networks have one grounded labeling In general, dependency networks may have • more than one grounded labeling,but this requires an even cycle • less than one grounded labeling,but this requires an odd cycle. Expert Systems 13

  20. Express that a and b are equivalent: a :- b. b :- a. The resulting network has two consistent labelings (both in or none in) but only the out-labeling is grounded Express that a and b are complimentary: a -: b. b -: a. The resulting network has two consistent labelings (a is in or b is in) and both are grounded a b Two ground or not two ground? a b Expert Systems 13

  21. c a b A Philosophical example: Teleology • Network 1: a :- b. b :- a.Has two consistent labelings, only one is grounded. • Network 2: c -: c.Has no consistent labeling. • Network 3: c -: c, b.Consistency requires a and b to be in • Only consistent labeling is not grounded Expert Systems 13

  22. The generality of Problem Solving Methods • Knowledge Acquisition Tools (SALT, MORE, RIME, …) were developed for a specific application • Application = Knowledge + Inferencer • Identifying and explicitizing the PSM allows to • Acquire knowledge more efficiently • Reuse the Problem Solving Method for other problems • That is very nice but….Knowledge is more valuable than Methods Can knowledge be reused over different applications? Expert Systems 13

  23. Protege: Knowledge and PSM Reuse Solve multiple problems on the same domain:- Elevator design, Elevator control, Elevator logistics- Molecule structure, Molecule interaction Protege approach: • Not only make theKA/PSM domain-independent • Make the KA alsoPSM/application-independent • Connect Domainknowledge to appli-cation throughmappings. Expert Systems 13

  24. Ontology: Model of knowledge Describe entities and relations, states, control knowledge An ontology is built for • Domain: stated in HE vocabulary • PSM: stated in developer’s vocabulary • Application Maitre: ontology editor Dash: compiles to KA Meditor: interpreter Marble: edit mappings Expert Systems 13

  25. Protege in the Large: Vertical Transport Applying Propose and Revise to Elevator domain knowledge was easy, because this knowledge was acquired for the purpose of P&R Expert Systems 13

  26. Protoge in the Small: Ribosome topology • From structural information about ribosome sequence, compute location of each. • Solution is a configuration, satisfying chemical and physical constraints. • A lot of knowledge on ribosomes is available: acquired for other purposes such as computing interactions. Expert Systems 13

  27. Application ontology for ribosome topology • Mapping relations:Supply the necessary application knowledge from existing domain knowledge • Missing knowledge:Specifically acquire extra knowledge needed in the application(Violation-fix) Conclusion:Reuse of ribosome knowledge over different applications is possible Gennari, Altman, Musen, 1995: Reuse with Protege-II: From Elevators to Ribosomes Expert Systems 13

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