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CHR + D + A + O Operational Semantics in Fluent Calculus

CHR + D + A + O Operational Semantics in Fluent Calculus. November, 2007. Simple Fluent Calculus (SFC). Introduction. A many-sorted first-order language with equality Includes: Sorts: FLUENT < STATE, ACTION, SIT Functions: Predicate. Abbreviations. Foundational Axioms (F state ).

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CHR + D + A + O Operational Semantics in Fluent Calculus

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  1. CHR + D + A + O Operational Semantics in Fluent Calculus November, 2007

  2. SimpleFluent Calculus (SFC)

  3. Introduction • A many-sorted first-order language with equality • Includes: • Sorts: FLUENT < STATE, ACTION, SIT • Functions: • Predicate

  4. Abbreviations

  5. Foundational Axioms (Fstate)

  6. SFC Domain Axiomatization • State Constraints • Unique simple Action Precondition Axiom for each function symbol with range ACTION • A set of State Update Axioms • Foundational Axioms (Fstate) • Possibly further domain-specific axioms

  7. Action Precondition Axiom • Ex:

  8. State Update Axiom • Ex:

  9. CHR Operational Semantics in Fluent Calculus

  10. Domain Sorts • RULE • Ex: gcd(0) <=> true | true. • CONSTRAINT • p(1,2,7) • UDC < CONSTRAINT • BIC < CONSTRAINT • EQUATION < BIC

  11. Domain Functions (1/2) • S0 :  SIT • The initial situation • InGoal : CONSTRAINT  FLUENT • The constraint x is in G • InUdc : UDC  FLUENT • The user defined constraint x is in U • InBic : BIC  FLUENT • The built-in constraint x is in B

  12. Domain Functions (2/2) • InPropHistory : RULE x Seq(UDC)  FLUENT • f = InPropHistory(r, p) • The propagation (r,p) is in the propagation history

  13. Domain Predicates (1/3) • InQuery : CONSTRAINT • The constraint is in the initial goal (query) • Matching : Seq(UDC) x Seq(UDC) x Set(EQUATION) x STATE • Matching(h, m, e, s) • The sequence of constraints m is in s and matches with h generating the matching equations in e

  14. Domain Predicates (2/3) • RenVars : RULE x RULE x STATE • RenVars(r, rc, s) • Rc is a copy of the rule r with all variables renamed (using names not already being used in s) • Ex: RenVars(“p(x)  q(x)”, “p(x1)  q(x1)”, s) • If x1 does not appear in s

  15. Domain Predicates (3/3) • entails : BIC x STATE x STATE x STATE • entails(s, c, s’+, s’-) • s’ = (s - s’-)o s’+ • CT |= (s ^ c  s’) • entails : STATE x Set(EQUATION) x Set(BIC) • entails(s, h, g) • CT |= s  \exists x(h ^ g)

  16. Domain Actions • Solve: BIC  ACTION • Introduce: UDC  ACTION • Simplify: RULE x Seq(UDC)  ACTION • Propagate: RULE x Seq(UDC) ACTION • Simpagate: RULE x Seq(UDC)x Seq(UDC)  ACTION

  17. Initial State (IS-Axiom)

  18. CHR Transitions

  19. Simpagate if (Hk / HR <=> G | B) in P and

  20. Simpagate if (Hk / HR <=> G | B) in P and

  21. CHR + DOperational Semantics in Fluent Calculus

  22. Nondeterminism in Fluent Calculus • Simple disjunctive state update axiom • θn is a first-order formula without terms of any reserved sort

  23. Domain Sorts • CHOICE < CONSTRAINT • (a1 ; ... ; an), where a1, ..., an are sets of CONSTRAINT • CHOICE = Set(Set(CONSTRAINT))

  24. Domain Actions • Split : CHOICE  ACTION

  25. Actions

  26. Split

  27. CHR + D + AOperational Semantics in Fluent Calculus

  28. Domain Sorts • JUSTIFICATION < CONSTRAINT

  29. Domain Functions • Just : CONSTRAINT x Set(JUSTIFICATION)  FLUENT • Just(c,j) • The constraint c is justified by the justifications in j • JustSet : Set(CONSTRAINT) x STATE  Set(JUSTIFICATION)

  30. Domain Predicates • entails : STATE x BIC x Set(FLUENT) x Set(FLUENT) • Assumptions: • every change in the built–in constraint store should be justified

  31. Domain Actions • AddConstraint : CONSTRAINT x JUSTIFICATION  ACTION • RemoveConstraint : Set(JUSTIFICATION)  ACTION

  32. Initial State

  33. State Constraints

  34. Actions

  35. AddConstraint

  36. RemoveConstraint

  37. Simpagate if (Hk / HR <=> G | B) in P and

  38. Split / Choice

  39. CHR + D + OOperational Semantics in Fluent Calculus

  40. Domain Sorts • FATOM < FMOLECULE < UDC • CANDIDATE • CLASS_CANDIDATE < CANDIDATE • CLASS x CLASS x FEATURE x VALUE • OBJECT_CANDIDATE < CANDIDATE • OBJECT x CLASS x FEATURE x VALUE

  41. Domain Predicates • ValidTaxonomy : STATE • TaxonomyCompletion : STATE x STATE • FeaturesCompletion : STATE x STATE • Candidate: CANDIDATE x STATE • ObjCandidate : OBJECT_CANDIDATE x STATE • ClassCandidate : CLASS_CANDIDATE x STATE • Candidate = ObjCandidate  ClassCandidate • Overriden : CANDIDATE x STATE

  42. Domain Axioms (1/2)

  43. Domain Axioms (2/2)

  44. Domain Actions • Inherit :  ACTION

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