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

CHR Operational Semantics in Fluent Calculus (using Ramifications)

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### CHR Operational Semantics in Fluent Calculus (using Ramifications)

### SimpleFluent Calculus (SFC)

### Ramifications in Fluent Calculus

November, 2007

Introduction

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

Foundational Axioms (Fstate)

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

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.)

- Causes(z1, e1+, e1-, z2, e2+, e2-)
- 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-

- Ramify(z, e+, e-, z’)

- Causes : STATE x STATE x STATE x STATE x STATE x STATE

Foundational Axioms

(Reflexive and Transitive Closure of Causes)

State Update Axiomwith Ramifications

Causal Relations Axiomatization

- 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

Domain Sorts

- CONSTRAINT < FLUENT
- UDC < CONSTRAINT
- BIC < CONSTRAINT
- EQUATION < BIC

Domain Predicates

- entails : STATE x Set(EQUATION) x Set(BIC)
- entails(s, h, g)
- CT |= s \exists x(h ^ g)

Domain Actions

- AddConstraint : CONSTRAINT ACTION

Example

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

Example(Constraint Awakening)

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