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# CHR Operational Semantics in Fluent Calculus (using Ramifications) - PowerPoint PPT Presentation

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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November, 2007

### SimpleFluent Calculus (SFC)

• A many-sorted first-order language with equality

• Includes:

• Sorts: FLUENT < STATE, ACTION, SIT

• Functions:

• Predicate

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

### Ramifications in Fluent Calculus

• 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-

(Reflexive and Transitive Closure of Causes)

State Update Axiomwith Ramifications

• Relies on the assumption that the underlying Causes relation is completely specified

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

### CHR Operational Semantics in Fluent Calculus

• CONSTRAINT < FLUENT

• UDC < CONSTRAINT

• BIC < CONSTRAINT

• EQUATION < BIC

• entails : STATE x Set(EQUATION) x Set(BIC)

• entails(s, h, g)

• CT |= s  \exists x(h ^ g)

• AddConstraint : CONSTRAINT  ACTION

leq(X,X) <=> true.

leq(X,Y), leq(Y,X) <=> X = Y.

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

leq(X,X) <=> true.

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

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

Example(Constraint Awakening)