CHR Operational Semantics in Fluent Calculus (using Ramifications)

1 / 24

# 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 &lt; STATE, ACTION, SIT Functions: Predicate. Abbreviations.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'CHR Operational Semantics in Fluent Calculus (using Ramifications)' - hada

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

November, 2007

### SimpleFluent Calculus (SFC)

Introduction
• 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

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-
Foundational Axioms

(Reflexive and Transitive Closure of Causes)

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

### CHR Operational Semantics in Fluent Calculus

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,X) <=> true.

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

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

Example

leq(X,X) <=> true.

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

Example

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