chr operational semantics in fluent calculus (using ramifications)
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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CHR Operational Semantics
in Fluent Calculus (using Ramifications)
November, 2007
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SimpleFluent Calculus (SFC)
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Introduction
• A many-sorted first-order language with equality• Includes:
– Sorts: FLUENT < STATE, ACTION, SIT
– Functions:
– Predicate
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Abbreviations
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Foundational Axioms (Fstate)
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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
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Action Precondition Axiom
• Ex:
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State Update Axiom
• Ex:
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Ramifications in Fluent Calculus
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Modeling Ramifications
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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-
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Abbreviations
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Foundational Axioms
(Reflexive and Transitive Closure of Causes)
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State Update Axiomwith Ramifications
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Causal Relations Axiomatization
• Relies on the assumption that the underlying Causes relation is completely specified
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Fluent Calculus Domain Axiomatization
with 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
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CHR Operational Semantics in Fluent Calculus
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Domain Sorts
• CONSTRAINT < FLUENT
• UDC < CONSTRAINT
• BIC < CONSTRAINT
• EQUATION < BIC
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Domain Predicates
• entails : STATE x Set(EQUATION) x Set(BIC)– entails(s, h, g)– CT |= s \exists x(h ^ g)
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Domain Actions
• AddConstraint : CONSTRAINT ACTION
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Example
leq(X,X) <=> true. leq(X,Y), leq(Y,X) <=> X = Y. leq(X,Y), leq(Y,Z) ==> leq(X,Z).
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Example
leq(X,X) <=> true.
leq(X,Y), leq(Y,Z) ==> leq(X,Z).
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Example
leq(X,Y), leq(Y,Z) ==> leq(X,Z).
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Example(Constraint Awakening)