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CHR Operational Semantics in Fluent Calculus (using Ramifications)

CHR Operational Semantics in Fluent Calculus (using Ramifications). November, 2007. Simple Fluent Calculus (SFC). Introduction. A many-sorted first-order language with equality Includes: Sorts: FLUENT < STATE, ACTION, SIT Functions: Predicate. Abbreviations.

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CHR Operational Semantics in Fluent Calculus (using Ramifications)

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  1. CHR Operational Semantics in Fluent Calculus (using Ramifications) 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. Ramifications in Fluent Calculus

  10. Modeling Ramifications

  11. Fluent Calculus with Ramifications • Sorted second-order logic language • Reserved Predicates: • Causes : STATE x STATE x STATE x STATE x STATE x STATE • Causes(z1, e1+, e1-, z2, e2+, e2-) • If z1 is the result of positive effects e1+ and negative effects e1-, then an additional effect is caused which leads to z2 (now the result of positive and negative effects e2+ and e2-, resp.) • Ramify : STATE x STATE x STATE x STATE • Ramify(z, e+, e-, z’) • z’ can be reached by iterated application of the underlying casual relation, starting in state z with momentum e+ and e-

  12. Abbreviations

  13. Foundational Axioms (Reflexive and Transitive Closure of Causes)

  14. State Update Axiomwith Ramifications

  15. Causal Relations Axiomatization • Relies on the assumption that the underlying Causes relation is completely specified

  16. Fluent Calculus Domain Axiomatizationwith Ramifications • State constraints • Causal Relations axiomatization • Unique action precondition axiom for each function symbol with range ACTION • Set of state update axioms (possibly with ramifications) • Foundational Axioms: Fstate and Framify • Domain Specific Axioms

  17. CHR Operational Semantics in Fluent Calculus

  18. Domain Sorts • CONSTRAINT < FLUENT • UDC < CONSTRAINT • BIC < CONSTRAINT • EQUATION < BIC

  19. Domain Predicates • entails : STATE x Set(EQUATION) x Set(BIC) • entails(s, h, g) • CT |= s  \exists x(h ^ g)

  20. Domain Actions • AddConstraint : CONSTRAINT  ACTION

  21. Example leq(X,X) <=> true. leq(X,Y), leq(Y,X) <=> X = Y. leq(X,Y), leq(Y,Z) ==> leq(X,Z).

  22. Example leq(X,X) <=> true. leq(X,Y), leq(Y,Z) ==> leq(X,Z).

  23. Example leq(X,Y), leq(Y,Z) ==> leq(X,Z).

  24. Example(Constraint Awakening)

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