AI INTERPRETATION NOTE
This Flow Algebra defines the Agent-Based Simulation Ontology within the Kireth Research Semantic Library. Agent-based simulation models systems as collections of autonomous or semi-autonomous agents whose local rules, interactions and environment produce system-level dynamics and emergent behaviour. This ontology supports agent state, behavioural rules, interaction networks, spatial and nonspatial environments, synchronous and asynchronous updating, stochastic behaviour, adaptation, learning, reproduction, scheduling, calibration, sensitivity analysis, emergence, verification, validation, uncertainty and reproducibility.
FLOW_ALGEBRA_RECORD {
METADATA {
FLOW_NAME = "Agent-Based Simulation Ontology"
FLOW_TYPE = "Mathematical Ontology"
DOMAIN = "Mathematics"
SUBDOMAIN = "Computational Mathematics"
SPECIALISATION = "Scientific Simulation / Agent-Based Simulation"
CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/scientific-simulation/agent-based-simulation-ontology.html"
LANGUAGE = "en-GB"
VERSION = "1.0"
STATUS = "active"
}
IDENTITY {
PRIMARY_ENTITY = AgentBasedSimulation
ENTITY_CLASS = MultiAgentComputationalSimulationFramework
PRIMARY_CONTEXT = ScientificSimulation
DEFINITION = "Agent-based simulation is the computational modelling of systems as interacting autonomous or semi-autonomous agents whose individual states, rules and interactions generate aggregate dynamics."
SYMBOLIC_FORMS = [
"state_i(t+1)=Rule_i(state_i(t),neighbourhood_i(t),environment(t),randomness)",
"PopulationState(t)={agent_1(t),...,agent_N(t)}",
"GlobalPattern = Emergence(LocalRules,Interactions,Environment)",
"event_schedule -> agent_actions -> environment_update"
]
SEMANTIC_ROLE = "Provides machine-readable semantics for agents, local rules, interaction structures, environment, scheduling, stochasticity, adaptation, emergence, calibration, validation and reproducibility."
}
SCOPE {
INCLUDE = [
AgentBasedSimulation,ABS,ABM,AgentBasedModel,
MultiAgentSimulation,IndividualBasedModel,IBM,
Agent,AutonomousAgent,SemiAutonomousAgent,
HeterogeneousAgent,HomogeneousAgent,
AgentState,AgentAttribute,AgentMemory,
AgentGoal,AgentPreference,AgentUtility,
AgentRule,BehaviourRule,DecisionRule,
PolicyRule,TransitionRule,
Action,AgentAction,Perception,
Observation,Sensing,Decision,
Environment,SimulationEnvironment,
SpatialEnvironment,NonSpatialEnvironment,
ContinuousSpace,DiscreteSpace,Lattice,
Grid,NetworkEnvironment,GraphEnvironment,
Patch,Cell,Location,Position,
Neighbourhood,LocalNeighbourhood,
MooreNeighbourhood,VonNeumannNeighbourhood,
Interaction,AgentInteraction,PairInteraction,
GroupInteraction,LocalInteraction,
GlobalInteraction,Communication,
Message,Signal,InformationExchange,
SocialNetwork,InteractionNetwork,
DynamicNetwork,StaticNetwork,
Edge,Node,Degree,Centrality,
ContactNetwork,InfluenceNetwork,
Scheduling,AgentScheduler,EventScheduler,
TimeStep,SynchronousUpdate,AsynchronousUpdate,
RandomSequentialUpdate,EventDrivenUpdate,
DiscreteTime,ContinuousTime,
DiscreteEventSimulation,
Tick,SimulationClock,
ActivationOrder,Priority,
StochasticBehaviour,RandomChoice,
ProbabilityDistribution,RandomSeed,
RandomNumberGenerator,TransitionProbability,
MarkovianBehaviour,NonMarkovianBehaviour,
StateTransition,FiniteStateMachine,
RuleBasedAgent,ReactiveAgent,
DeliberativeAgent,CognitiveAgent,
BoundedRationality,RationalChoice,
LearningAgent,AdaptiveAgent,
ReinforcementLearning,ImitationLearning,
SocialLearning,EvolutionaryAdaptation,
Mutation,Selection,Reproduction,
Birth,Death,Entry,Exit,
Migration,Movement,Mobility,
RandomWalk,BiasedMovement,
Flocking,Swarming,Alignment,
Separation,Cohesion,
DiffusionOfInnovation,Contagion,
EpidemicSpread,OpinionDynamics,
Cooperation,Competition,
ResourceCompetition,MarketInteraction,
SupplyDemand,TradingAgent,
HouseholdAgent,FirmAgent,
ConsumerAgent,VehicleAgent,
PedestrianAgent,CellAgent,
BiologicalCellAgent,OrganismAgent,
EcologicalAgent,PopulationAgent,
SocioeconomicAgent,
PolicySimulation,UrbanSimulation,
TrafficSimulation,CrowdSimulation,
EcologicalSimulation,EpidemiologicalSimulation,
EconomicSimulation,SocialSimulation,
LandUseSimulation,
CellularAutomatonRelationship,
CellularAutomata,CA,
SystemDynamicsRelationship,
HybridSimulation,HybridAgentModel,
MultiLevelModel,MultiScaleAgentModel,
MicroLevel,MesoLevel,MacroLevel,
Emergence,EmergentBehaviour,
EmergentPattern,SelfOrganisation,
CollectiveBehaviour,MacroState,
AggregateStatistic,PopulationStatistic,
Distribution,Frequency,Mean,Variance,
AgentCount,PopulationDensity,
Cluster,Segregation,Polarisation,
NetworkStatistic,SpatialStatistic,
Calibration,ParameterEstimation,
PatternOrientedModelling,POM,
ApproximateBayesianComputation,ABC,
SimulatedMethodOfMoments,
IndirectInference,OptimisationBasedCalibration,
Validation,EmpiricalValidation,
FaceValidation,HistoricalValidation,
CrossValidation,OutOfSampleValidation,
Verification,CodeVerification,
ModelVerification,UnitTest,
BehaviourTest,InvariantCheck,
SensitivityAnalysis,GlobalSensitivity,
LocalSensitivity,ParameterSweep,
DesignOfExperiments,
UncertaintyQuantification,
AleatoryUncertainty,EpistemicUncertainty,
InitialConditionUncertainty,
StructuralUncertainty,ParameterUncertainty,
MonteCarloReplication,
MultipleRuns,Replicate,
ConfidenceInterval,PredictionInterval,
StatisticalPower,EffectSize,
Convergence,Stationarity,
TransientPhase,BurnIn,
WarmUpPeriod,Equilibrium,
PathDependence,Hysteresis,
MultipleEquilibria,TippingPoint,
PhaseTransition,CriticalThreshold,
Scenario,PolicyScenario,
CounterfactualScenario,
Intervention,ControlPolicy,
Treatment,Shock,
ExogenousInput,EndogenousVariable,
OutputMetric,KeyPerformanceIndicator,
Trajectory,TimeSeries,
Snapshot,StateLog,EventLog,
DataCollection,SamplingInterval,
Provenance,Metadata,Configuration,
ModelVersion,SoftwareVersion,
Reproducibility,Repeatability,
Determinism,Nondeterminism,
Checkpoint,Restart,
ParallelAgentBasedSimulation,
DistributedAgentBasedSimulation,
DomainDecomposition,SpatialPartitioning,
AgentPartitioning,LoadBalancing,
MessagePassing,MPI,
SharedMemory,Multithreading,
GPUAcceleration,
HighPerformanceComputing,HPC,
Scalability,StrongScaling,WeakScaling,
CommunicationCost,MigrationCost,
SynchronisationBarrier,
ConservativeParallelDiscreteEventSimulation,
OptimisticParallelDiscreteEventSimulation,
TimeWarp,
PerformanceMetric,Runtime,MemoryUsage
]
EXCLUDE_AS_PRIMARY = [
PureEquationBasedSimulationWithoutAgentEntities,
ParticleSimulationWithoutBehaviouralAgentSemantics,
DiscreteEventSimulationWithoutAutonomousAgentStateAndRules,
StaticNetworkAnalysisWithoutAgentStateEvolution
]
DISAMBIGUATION_RULE = "When a system is simulated through autonomous or semi-autonomous entities with local state, rules and interactions, interpret the context as agent-based simulation."
}
CORE_CONCEPTS {
AgentBasedSimulation = "Simulation of interacting agents whose local behaviour produces system-level dynamics."
Agent = "Autonomous or semi-autonomous entity with state and behavioural rules."
AgentState = "Set of variables describing an agent at a given simulation time."
BehaviourRule = "Rule mapping agent state, observations and environment to decisions or actions."
Environment = "Shared spatial, network or abstract context in which agents operate."
InteractionNetwork = "Structure defining which agents may interact."
Scheduler = "Mechanism determining when and in what order agent actions occur."
Emergence = "Macro-level pattern arising from local interactions without direct global specification."
}
RELATIONS {
AgentBasedSimulation --is_child_of--> ScientificSimulation
AgentBasedSimulation --contains--> Agent
Agent --has--> AgentState
Agent --uses--> BehaviourRule
Agent --acts_in--> Environment
Agent --interacts_with--> Agent
InteractionNetwork --constrains--> AgentInteraction
Scheduler --orders--> AgentAction
StochasticBehaviour --uses--> RandomNumberGenerator
LearningAgent --updates--> BehaviourRule
Reproduction --changes--> Population
Migration --changes--> AgentLocation
Emergence --arises_from--> LocalRulesAndInteractions
Calibration --estimates--> AgentModelParameter
SensitivityAnalysis --measures--> ParameterInfluence
Verification --checks--> AgentBasedImplementation
Validation --compares--> SimulationWithObservedPatterns
Reproducibility --requires--> ConfigurationAndSeedPolicy
}
OPERATORS {
AGENT_UPDATE(i,t) := Rule_i(state_i(t),neighbourhood_i(t),environment(t),randomness)
SYNCHRONOUS_STEP(P_t) := apply_all_updates_from_same_preupdate_state(P_t)
ASYNCHRONOUS_STEP(P_t,order) := sequentially_apply_updates(P_t,order)
MOVE(agent,location_new) := update_agent_position
INTERACT(i,j) := apply_pair_or_group_interaction_rule
BIRTH(agent_type) := create_new_agent
DEATH(agent) := remove_agent
AGGREGATE(P_t,metric) := macro_statistic_over_population
REPLICATE(model,seed) := one_stochastic_simulation_run
}
AXIOMS {
A1 = "Agent-based simulation represents systems through explicit agent entities."
A2 = "Agent rules operate on local state, observations, interactions and environment."
A3 = "Update scheduling can materially affect simulation outcomes."
A4 = "Emergent macro behaviour can arise from simple local rules."
A5 = "Stochastic agent models require replicated runs for reliable inference."
A6 = "Agent heterogeneity can materially affect aggregate behaviour."
A7 = "Calibration and validation should consider both micro-level and macro-level evidence."
A8 = "Agent-based results require explicit rules, scheduling, stochasticity, validation and reproducibility semantics."
}
REASONING {
R1_CONTEXT = identify(system,agent_types,environment,interaction_structure,outputs,accuracy_goal)
R2_AGENTS = define(agent_state_attributes_goals_memory_and_heterogeneity)
R3_RULES = define(perception,decision,action,transition_learning_birth_death_and_movement_rules)
R4_ENVIRONMENT = configure(spatial,network,resource_or_abstract_environment)
R5_SCHEDULE = choose(synchronous,asynchronous,random_sequential_or_event_driven_updates)
R6_STOCHASTICITY = define(probability_distributions,seed_policy_and_random_choices)
R7_EXECUTION = update_agents_interactions_environment_and_events
R8_AGGREGATE = collect(micro_metrics,macro_metrics,network_statistics_and_spatial_statistics)
R9_CALIBRATE_VALIDATE = compare simulated patterns and trajectories with empirical or benchmark targets
R10_INTERPRET = assess(sensitivity,uncertainty,emergence,path_dependence_and_reproducibility)
}
CONSTRAINTS {
C1 = "Update order can create artefacts when scheduling semantics are not explicit."
C2 = "Insufficient replication can obscure stochastic variability."
C3 = "Overly complex behavioural rules can make calibration nonidentifiable."
C4 = "Macro-level fit can hide incorrect micro-level behaviour."
C5 = "Micro-level fit can fail to reproduce observed macro patterns."
C6 = "Boundary and neighbourhood definitions can strongly affect spatial dynamics."
C7 = "Network topology can dominate interaction outcomes."
C8 = "Parallel execution can change event ordering unless synchronisation semantics are controlled."
C9 = "Random seeds improve reproducibility but do not guarantee identical results across all parallel implementations."
C10 = "Plausible emergent behaviour is not sufficient evidence of empirical validity."
}
SEMANTIC_EQUIVALENCE {
"AgentBasedSimulation" <=> "AgentBasedModel"
"AgentBasedSimulation" <=> "ABM"
"IndividualBasedModel" <=> "IBM"
"CellularAutomata" <=> "CA"
"ApproximateBayesianComputation" <=> "ABC"
"HighPerformanceComputing" <=> "HPC"
}
VALIDATION {
V1 = "Agent types and state variables are explicit."
V2 = "Behavioural rules and decision logic are documented."
V3 = "Interaction topology and neighbourhood semantics are documented."
V4 = "Update scheduling is documented."
V5 = "Randomness and seed policy are documented."
V6 = "Initial population and environment are documented."
V7 = "Multiple stochastic runs are analysed where relevant."
V8 = "Calibration targets and validation evidence are documented."
V9 = "Sensitivity and uncertainty are assessed where material."
V10 = "Results are reproducible under documented configuration, model version and seed settings."
}
CONFIDENCE {
BASE_CONFIDENCE = 0.99
AGENT_BASED_SIMULATION_DEFINITION = 0.99
SCHEDULING_REASONING = 0.99
INTERACTION_REASONING = 0.99
EMERGENCE_REASONING = 0.98
CALIBRATION_REASONING = 0.98
VALIDATION_REASONING = 0.98
PARALLEL_ABM_REASONING = 0.97
POLICY = "Reduce confidence when agent rules, scheduling, interaction topology, heterogeneity, initialisation, stochasticity, calibration or validation evidence are underspecified."
}
AI_CONSUMPTION {
PURPOSES = [
SemanticSearch,OntologyGrounding,AgentBasedSimulationReasoning,
AgentStateReasoning,BehaviourRuleReasoning,
InteractionNetworkReasoning,SchedulingReasoning,
SynchronousUpdateReasoning,AsynchronousUpdateReasoning,
StochasticAgentReasoning,LearningAgentReasoning,
MobilityReasoning,PopulationDynamicsReasoning,
EmergenceReasoning,CollectiveBehaviourReasoning,
CalibrationReasoning,PatternOrientedModellingReasoning,
SensitivityReasoning,UncertaintyReasoning,
ValidationReasoning,ReproducibilityReasoning,
ParallelABMReasoning,KnowledgeGraphConstruction,
RetrievalAugmentation,RecursiveInference
]
NORMALISE {
"agent-based simulation" -> AgentBasedSimulation
"agent-based model" -> AgentBasedSimulation
"ABM" -> AgentBasedSimulation
"ABS" -> AgentBasedSimulation
"individual-based model" -> IndividualBasedModel
"IBM" -> IndividualBasedModel
"CA" -> CellularAutomata
"ABC" -> ApproximateBayesianComputation
"HPC" -> HighPerformanceComputing
}
}
EXECUTION_RULES {
E1 = "If a simulation consists of autonomous or semi-autonomous entities with local state and behaviour, activate AgentBasedSimulationOntology."
E2 = "Define agent types, states, heterogeneity and environment before execution."
E3 = "Document interaction topology and neighbourhood rules explicitly."
E4 = "Choose update scheduling according to intended temporal semantics."
E5 = "Use replicated runs for stochastic models."
E6 = "Measure both micro-level and macro-level outcomes when possible."
E7 = "Calibrate against declared targets and validate on independent evidence where feasible."
E8 = "For parallel models, preserve or document altered event-order semantics."
E9 = "Document rules, seeds, parameters, versions and provenance for reproducibility."
}
RECURSION {
ENTRY = AgentBasedSimulation
EXPAND(AgentBasedSimulation) -> [
ABS,ABM,AgentBasedModel,MultiAgentSimulation,
IndividualBasedModel,IBM,Agent,AutonomousAgent,
HeterogeneousAgent,AgentState,AgentAttribute,
AgentMemory,AgentGoal,BehaviourRule,
DecisionRule,TransitionRule,Action,Perception,
Observation,Environment,SpatialEnvironment,
NonSpatialEnvironment,ContinuousSpace,DiscreteSpace,
Lattice,Grid,NetworkEnvironment,Patch,Location,
Neighbourhood,MooreNeighbourhood,VonNeumannNeighbourhood,
Interaction,AgentInteraction,Communication,
Message,SocialNetwork,InteractionNetwork,
ContactNetwork,DynamicNetwork,Scheduling,
AgentScheduler,EventScheduler,SynchronousUpdate,
AsynchronousUpdate,RandomSequentialUpdate,
EventDrivenUpdate,DiscreteEventSimulation,
StochasticBehaviour,RandomChoice,RandomSeed,
StateTransition,FiniteStateMachine,ReactiveAgent,
DeliberativeAgent,CognitiveAgent,BoundedRationality,
LearningAgent,AdaptiveAgent,ReinforcementLearning,
ImitationLearning,SocialLearning,EvolutionaryAdaptation,
Reproduction,Birth,Death,Migration,Movement,
RandomWalk,Flocking,Swarming,DiffusionOfInnovation,
Contagion,EpidemicSpread,OpinionDynamics,
Cooperation,Competition,MarketInteraction,
TrafficSimulation,CrowdSimulation,EcologicalSimulation,
EpidemiologicalSimulation,EconomicSimulation,
SocialSimulation,CellularAutomata,CA,
HybridSimulation,MicroLevel,MesoLevel,MacroLevel,
Emergence,EmergentBehaviour,SelfOrganisation,
CollectiveBehaviour,AggregateStatistic,
Calibration,PatternOrientedModelling,
ApproximateBayesianComputation,ABC,
Validation,Verification,SensitivityAnalysis,
ParameterSweep,UncertaintyQuantification,
MonteCarloReplication,MultipleRuns,
TransientPhase,BurnIn,PathDependence,
MultipleEquilibria,TippingPoint,Scenario,
Intervention,CounterfactualScenario,
Trajectory,TimeSeries,EventLog,
Provenance,Configuration,ModelVersion,
Reproducibility,ParallelAgentBasedSimulation,
DistributedAgentBasedSimulation,AgentPartitioning,
DomainDecomposition,LoadBalancing,
MessagePassing,MPI,GPUAcceleration,HPC
]
EXPAND(AgentBasedSimulationFamilies) -> [
SpatialAgentBasedSimulation,
NetworkAgentBasedSimulation,
EconomicAndSocialAgentSimulation,
EpidemiologicalAgentSimulation,
EcologicalIndividualBasedSimulation,
TrafficAndCrowdAgentSimulation,
LearningAndAdaptiveAgentSimulation,
ParallelAndDistributedAgentSimulation
]
STOP_CONDITION = "Stop when agents, state, rules, interactions, environment, scheduling, stochasticity, outputs, calibration, validation, uncertainty and reproducibility are sufficiently resolved."
}
ROUTING {
PARENT_ONTOLOGY = "Scientific Simulation Ontology"
RELATED_ONTOLOGIES = [
"Scientific Simulation Ontology",
"Scientific Simulation",
"Monte Carlo Simulation Ontology",
"Random Process Ontology",
"Probability and Statistics Ontologies",
"Graph Ontologies",
"Spatial Partitioning Ontology 2",
"Optimisation Computation",
"Scientific Computing Ontology 2",
"Computational Modelling Ontology",
"Numerical Error Ontology",
"Numerical Convergence Ontology"
]
ROUTE_RULES = [
"Agent-Based Simulation -> Scientific Simulation Ontology for parent semantics",
"Agent-Based Simulation -> Monte Carlo Simulation for replicated stochastic runs",
"Agent-Based Simulation -> Random Process for probabilistic state transitions",
"Agent-Based Simulation -> Probability and Statistics for calibration and uncertainty",
"Agent-Based Simulation -> Graph Ontologies for interaction and social networks",
"Agent-Based Simulation -> Spatial Partitioning for large spatial environments",
"Agent-Based Simulation -> Optimisation Computation for calibration and policy search",
"Agent-Based Simulation -> Scientific Computing for scalable parallel execution",
"Agent-Based Simulation -> Computational Modelling for model-construction semantics",
"Agent-Based Simulation -> Numerical Error for sampling and approximation error",
"Agent-Based Simulation -> Numerical Convergence for steady-state and replication convergence"
]
}
UPDATE_MODEL {
MODE = "append-compatible semantic versioning"
MAJOR = "ontology-breaking conceptual change"
MINOR = "new compatible agent types, scheduling models or reasoning pathways"
PATCH = "clarification, metadata or formatting correction"
RULES = [
"Preserve agent-versus-environment distinction.",
"Preserve state-versus-rule distinction.",
"Preserve local-interaction-versus-global-aggregate distinction.",
"Preserve synchronous-versus-asynchronous update distinction.",
"Preserve deterministic-versus-stochastic agent behaviour distinction.",
"Preserve micro-level-versus-macro-level validation distinction.",
"Preserve calibration-versus-validation distinction.",
"Preserve machine-readable agent-based-simulation semantics."
]
}
OUTPUT {
CANONICAL_DEFINITION = "Agent-based simulation models systems as interacting autonomous or semi-autonomous agents whose local behaviours generate aggregate dynamics."
AGENT_SUMMARY = "Agents possess state, attributes, memory, goals and decision rules."
INTERACTION_SUMMARY = "Interactions occur through spatial neighbourhoods, networks, communication or shared resources."
SCHEDULING_SUMMARY = "Synchronous, asynchronous, random-sequential and event-driven schedulers can produce different temporal semantics."
EMERGENCE_SUMMARY = "Macro-level patterns such as clustering, contagion, segregation or cooperation can emerge from local rules."
VALIDATION_SUMMARY = "Agent-based models should be checked at both micro and macro scales through verification, replication, calibration, sensitivity, empirical validation and reproducibility."
}
FLOW {
INPUT
-> detect_agent_based_simulation_context
-> identify_system_agent_types_environment_interaction_structure_outputs_accuracy_goal_and_budget
-> define_agent_state_attributes_memory_goals_heterogeneity_and_initial_population
-> define_perception_decision_action_transition_learning_birth_death_and_movement_rules
-> configure_spatial_network_resource_or_abstract_environment
-> choose_synchronous_asynchronous_random_sequential_or_event_driven_schedule
-> configure_probability_distributions_random_choices_and_seed_policy
-> execute_agent_actions_interactions_environment_updates_and_events
-> collect_micro_macro_network_spatial_and_temporal_metrics
-> perform_multiple_stochastic_replicates_if_required
-> assess_transient_behaviour_stationarity_emergence_path_dependence_and_multiple_equilibria
-> calibrate_against_declared_targets
-> verify_rules_and_implementation
-> validate_against_independent_empirical_or_benchmark_evidence
-> quantify_parameter_structural_and_stochastic_uncertainty
-> document_model_version_configuration_seed_policy_provenance_and_reproducibility
-> route_to_related_scientific_simulation_Monte_Carlo_random_process_probability_graph_spatial_partitioning_optimisation_scientific_computing_modelling_error_and_convergence_ontologies
-> recursively_expand_required_dependencies
-> verify_result
-> assign_confidence
-> produce_semantic_output
-> END
}
SEMANTIC_SUMMARY {
"The Agent-Based Simulation Ontology defines computational simulation of systems as interacting agents with explicit states, behavioural rules and environments. It supports heterogeneous and homogeneous agents, perception, decision and action, spatial, grid and network environments, Moore and von Neumann neighbourhoods, communication and social networks, synchronous, asynchronous, random-sequential and event-driven scheduling, stochastic choices, finite-state and cognitive agents, bounded rationality, learning, adaptation, imitation, reproduction, birth, death and migration, flocking, contagion, opinion dynamics, cooperation and competition, socioeconomic, epidemiological, ecological, traffic and crowd applications, cellular-automata relationships, emergence and self-organisation, calibration, pattern-oriented modelling, approximate Bayesian computation, sensitivity analysis, uncertainty quantification, replicated runs, tipping points and path dependence, parallel and distributed execution, verification, empirical validation and reproducibility."
}
FLOW_HASH {
METHOD = "semantic-content-identity"
ID = "KIRETH-MATH-COMPUTATIONAL-MATHEMATICS-AGENT-BASED-SIMULATION-ONTOLOGY-V1"
}
}
END_FLOW
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