UOR Interaction Algebra

IRI: https://uor.foundation/interaction/
Prefix: interaction:
Space: bridge
Comment: Multi-entity interaction: commutator states, associator triples, negotiation convergence.

Imports

https://uor.foundation/op/
https://uor.foundation/convergence/
https://uor.foundation/state/
https://uor.foundation/observable/
https://uor.foundation/schema/

Classes

Name	IRI	Subclass Of	Comment
InteractionContext	`https://uor.foundation/interaction/InteractionContext`	`http://www.w3.org/2002/07/owl#Thing`	Two entities sharing sites through composed operations. Properties: entityA, entityB, sharedSiteMask, commutatorNorm.
CommutatorState	`https://uor.foundation/interaction/CommutatorState`	`http://www.w3.org/2002/07/owl#Thing`	The norm ‖[δ_A, ι_B]‖ on shared sites. Zero iff operators commute on the shared domain.
AssociatorState	`https://uor.foundation/interaction/AssociatorState`	`http://www.w3.org/2002/07/owl#Thing`	The norm of the three-way associator on shared sites.
AssociatorTriple	`https://uor.foundation/interaction/AssociatorTriple`	`http://www.w3.org/2002/07/owl#Thing`	Three entities whose interaction exhibits non-associativity due to read-write interleaving.
ThreeWaySite	`https://uor.foundation/interaction/ThreeWaySite`	`http://www.w3.org/2002/07/owl#Thing`	A site shared by all three entities in an AssociatorTriple.
NegotiationTrace	`https://uor.foundation/interaction/NegotiationTrace`	`http://www.w3.org/2002/07/owl#Thing`	Sequence of CommutatorStates across interaction steps.
MutualModelTrace	`https://uor.foundation/interaction/MutualModelTrace`	`http://www.w3.org/2002/07/owl#Thing`	Sequence of AssociatorStates across interaction steps.
InteractionNerve	`https://uor.foundation/interaction/InteractionNerve`	`http://www.w3.org/2002/07/owl#Thing`	Simplicial complex of N-entity coupling.
InteractionComposition	`https://uor.foundation/interaction/InteractionComposition`	`http://www.w3.org/2002/07/owl#Thing`	IC(A,B) = κ(session(A,B)). Combined interaction-composition operator.

Properties

Name	Kind	Functional	Domain	Range	Comment
entityA	Object	true	`https://uor.foundation/interaction/InteractionContext`	`https://uor.foundation/schema/TermExpression`	First entity in the interaction context.
entityB	Object	true	`https://uor.foundation/interaction/InteractionContext`	`https://uor.foundation/schema/TermExpression`	Second entity in the interaction context.
sharedSiteMask	Datatype	true	`https://uor.foundation/interaction/InteractionContext`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Bitmask identifying which sites are shared between the two entities.
commutatorNorm	Datatype	true	`https://uor.foundation/interaction/InteractionContext`	`http://www.w3.org/2001/XMLSchema#decimal`	The norm of the commutator on shared sites. Zero iff the operators commute.
commutatorValue	Datatype	true	`https://uor.foundation/interaction/CommutatorState`	`http://www.w3.org/2001/XMLSchema#decimal`	The computed commutator norm value.
associatorNorm	Datatype	true	`https://uor.foundation/interaction/AssociatorState`	`http://www.w3.org/2001/XMLSchema#decimal`	The norm of the three-way associator on shared sites.
tripleComponentA	Object	true	`https://uor.foundation/interaction/AssociatorTriple`	`https://uor.foundation/schema/Datum`	First component datum in the associator triple.
tripleComponentB	Object	true	`https://uor.foundation/interaction/AssociatorTriple`	`https://uor.foundation/schema/Datum`	Second component datum in the associator triple.
tripleComponentC	Object	true	`https://uor.foundation/interaction/AssociatorTriple`	`https://uor.foundation/schema/Datum`	Third component datum in the associator triple.
sitePosition	Datatype	true	`https://uor.foundation/interaction/ThreeWaySite`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The position index of the shared site.
leftGroupingValue	Datatype	true	`https://uor.foundation/interaction/ThreeWaySite`	`http://www.w3.org/2001/XMLSchema#decimal`	Value under left-associative grouping (AB)C.
rightGroupingValue	Datatype	true	`https://uor.foundation/interaction/ThreeWaySite`	`http://www.w3.org/2001/XMLSchema#decimal`	Value under right-associative grouping A(BC).
isPinned	Datatype	true	`https://uor.foundation/interaction/ThreeWaySite`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this site is pinned by a lease constraint.
pinningPair	Object	true	`https://uor.foundation/interaction/ThreeWaySite`	`https://uor.foundation/schema/TermExpression`	Identifier of the entity pair that pins this site.
negotiationSteps	Datatype	true	`https://uor.foundation/interaction/NegotiationTrace`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Number of steps in the negotiation trace.
isConvergent	Datatype	true	`https://uor.foundation/interaction/NegotiationTrace`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether the trace converges to zero commutator or zero associator.
modelConvergent	Datatype	true	`https://uor.foundation/interaction/MutualModelTrace`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether the mutual model trace converges.
nerveDimension	Datatype	true	`https://uor.foundation/interaction/InteractionNerve`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Maximum dimension of the interaction nerve simplicial complex.
nerveBettiNumbers	Datatype	true	`https://uor.foundation/interaction/InteractionNerve`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Betti number sequence of the interaction nerve.
reificationDepth	Datatype	true	`https://uor.foundation/interaction/InteractionComposition`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Depth of the interaction composition reification.
traceLength	Datatype	true	`https://uor.foundation/interaction/NegotiationTrace`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of steps in a negotiation trace.
convergenceRate	Datatype	true	`https://uor.foundation/interaction/NegotiationTrace`	`http://www.w3.org/2001/XMLSchema#decimal`	The rate at which the negotiation trace converges.
terminalValue	Object	true	`https://uor.foundation/interaction/NegotiationTrace`	`https://uor.foundation/schema/TermExpression`	The terminal value of the negotiation trace.
associatorProfileRef	Object	true	`https://uor.foundation/interaction/AssociatorTriple`	`https://uor.foundation/observable/Observable`	Reference to the observable describing the associativity profile.
associatorNormValue	Datatype	true	`https://uor.foundation/interaction/AssociatorTriple`	`http://www.w3.org/2001/XMLSchema#decimal`	The maximum norm of the associator for this triple.