Chr operational semantics in fluent calculus using ramifications
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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

CHR Operational Semantics in Fluent Calculus (using Ramifications)

November, 2007


Simple fluent calculus sfc

SimpleFluent Calculus (SFC)


Introduction
Introduction

  • A many-sorted first-order language with equality

  • Includes:

    • Sorts: FLUENT < STATE, ACTION, SIT

    • Functions:

    • Predicate




Sfc domain axiomatization
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

Ramifications in Fluent Calculus



Fluent calculus with ramifications
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
Foundational Axioms

(Reflexive and Transitive Closure of Causes)


State update axiom with ramifications
State Update Axiomwith Ramifications


Causal relations axiomatization
Causal Relations Axiomatization

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


Fluent calculus domain axiomatization with ramifications
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
Domain Sorts

  • CONSTRAINT < FLUENT

  • UDC < CONSTRAINT

  • BIC < CONSTRAINT

  • EQUATION < BIC


Domain predicates
Domain Predicates

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

    • entails(s, h, g)

    • CT |= s  \exists x(h ^ g)


Domain actions
Domain Actions

  • AddConstraint : CONSTRAINT  ACTION


Example
Example

leq(X,X) <=> true.

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

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


Example1
Example

leq(X,X) <=> true.

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


Example2
Example

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


Example constraint awakening
Example(Constraint Awakening)


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