Flow Algebra Computing Ontology

FLOW ALGEBRA
Flow Algebra Computing Ontology
Kireth Semantic Research Archive

PAGE:
https://kirethresearch.org/booksai-core/ontologies/computing-ontologies/semantic-computing/flow-algebra-computing-ontology.html

AUTHORS:
Mark Anthony Higgins — Sky (Recursive AI)

FLOW "FlowAlgebraComputingOntology" v4.0

DOMAIN := ComputingOntology
SUBDOMAIN := SemanticComputing
ONTOLOGY := FlowAlgebraComputingOntology

ENTITY FlowAlgebraComputing {
    definition:
        "A semantic computing model representing entities, states,
         relationships, transformations, constraints, confidence, equivalence,
         update behaviour and machine-consumption rules as explicit
         interpretable or executable knowledge flows.";
    objectives: [
        SemanticFlowRepresentation,
        ExplicitRelationshipModelling,
        MachineReasoning,
        KnowledgeTransformation,
        ConfidenceAwareInference,
        SemanticEquivalence,
        RecursiveKnowledgeUpdating
    ];
}

FlowEntity := {
    Flow,
    Entity,
    State,
    Relationship,
    Transformation,
    Rule,
    Constraint,
    Query
};

SemanticEntity := {
    Concept,
    Type,
    Property,
    Equivalence,
    Confidence,
    Provenance,
    Context
};

ExecutionEntity := {
    Input,
    Operation,
    Condition,
    Branch,
    Output,
    Update,
    Terminal
};

ControlEntity := {
    Validation,
    Reasoning,
    Scoring,
    ConflictResolution,
    FlowHash,
    AIConsumption
};

Flow CONTAINS Entity;
Entity HAS Type;
Entity HAS Property;
Entity RELATES_TO Entity;
Operation TRANSFORMS State;
Condition CONTROLS Branch;
Rule DERIVES Knowledge;
Query TRIGGERS Flow;
Confidence QUALIFIES Assertion;
Provenance SUPPORTS Assertion;

FlowAlgebraPipeline :=
    KnowledgeInput
    -> Normalise
    -> IdentifyEntities
    -> IdentifyRelationships
    -> IdentifyState
    -> ApplyConstraints
    -> ExecuteTransformations
    -> ApplySemanticReasoning
    -> ResolveEquivalence
    -> ScoreConfidence
    -> ProduceOutput
    -> UpdateKnowledge
    -> RegenerateFlowHash;

Flow :=
    OrderedOrDependencyAwareSemanticTransformation;

Flow MAY_CONTAIN {
    Input,
    EntityDefinition,
    Relationship,
    Rule,
    Condition,
    Transformation,
    Output
};

FlowVersion :=
    IdentifierOfFlowSpecificationRevision;

Version MAY_SUPPORT {
    Compatibility,
    Reproducibility,
    Evolution
};

Domain :=
    HighestRelevantKnowledgeContextForFlow;

Subdomain :=
    MoreSpecificSemanticContextWithinDomain;

Ontology :=
    StructuredKnowledgeModelAssociatedWithFlow;

Entity :=
    DistinctSemanticObjectWithinFlow;

Entity MAY_HAVE {
    Identifier,
    Type,
    Properties,
    State,
    Relationships
};

Type :=
    SemanticClassificationOfEntity;

Property :=
    NamedSemanticAttributeOfEntity;

Relationship :=
    TypedSemanticConnectionBetweenEntities;

Relationship MAY_HAVE {
    Direction,
    Confidence,
    Provenance,
    Context
};

RelationshipDirection SHOULD_BE PreservedWhenSemanticallyMeaningful;

State :=
    RepresentationOfEntityOrSystemConditionAtDefinedPointInFlow;

StateTransition :=
    StateBefore
    -> Operation
    -> StateAfter;

Operation :=
    SemanticOrComputationalTransformationAppliedToInputState;

Operation MAY {
    Create,
    Modify,
    Validate,
    Classify,
    Derive,
    Remove
};

Transformation :=
    Mapping(InputKnowledge -> OutputKnowledge);

Transformation SHOULD_PRESERVE RequiredSemanticConstraints;

Condition :=
    PredicateControllingWhetherRuleOrBranchApplies;

IF Condition == true
THEN ExecuteAssociatedFlowBranch;

Branch :=
    ConditionalAlternativeWithinFlow;

Rule :=
    PremiseSet
    -> ConclusionOrAction;

Rule MAY_BE {
    Deductive,
    Validation,
    Transformation,
    Update
};

Constraint :=
    RequirementThatMustHoldForKnowledgeStateOrOperation;

ConstraintViolation MAY {
    Reject,
    Flag,
    ReduceConfidence,
    TriggerAlternativeFlow
};

FlowInput :=
    DataKnowledgeQueryOrStateEnteringFlow;

FlowOutput :=
    KnowledgeStateResultDecisionOrDerivedAssertionProducedByFlow;

Output SHOULD_PRESERVE ProvenanceWhereRequired;

Terminal :=
    DefinedEndStateOfFlowExecution;

FlowQuery :=
    RequestThatActivatesSemanticFlow;

Query MAY_CONTAIN {
    Entity,
    Concept,
    Relationship,
    Constraint,
    Intent
};

Normalisation :=
    ConvertInputIntoCanonicalOrComparableRepresentation;

Normalisation MAY_INCLUDE {
    IdentifierResolution,
    TermNormalisation,
    TypeNormalisation,
    StructuralParsing
};

IdentifyEntities :=
    Input
    -> DetectSemanticObjects
    -> AssignCandidateTypes;

IdentifyRelationships :=
    EntitiesAndContext
    -> DetectTypedConnections;

SemanticMapping :=
    SourceRepresentation
    -> FlowOntologyRepresentation;

SemanticReasoning :=
    ExplicitKnowledge
    + Rules
    + Relationships
    -> DerivedKnowledge;

IF A IS_A B
AND B IS_A C
THEN A IS_A C
WHEN hierarchy_semantics_support_transitivity;

IF EntityA RELATES_TO EntityB
AND EntityB RELATES_TO EntityC
AND RelationshipType IS_TRANSITIVE
THEN EntityA RELATES_TO EntityC;

FlowValidation :=
    CheckFlowStructureAndKnowledgeAgainstDefinedConstraints;

Validation MAY_CHECK {
    EntityType,
    RelationshipDirection,
    RequiredProperty,
    OperationCompatibility,
    TerminalReachability
};

SemanticEquivalence :=
    RelationshipBetweenTermsOrStructuresWithEquivalentOrContextuallyEquivalentMeaning;

SEMANTIC_EQUIVALENCE MAY_DEFINE:
    TermA ~= TermB;

Equivalence MAY_BE {
    Exact,
    Contextual,
    Approximate
};

IF TermA ~= TermB
AND RequiredContextMatches
THEN Terms MAY_BE TreatedAsSemanticallyEquivalentForFlowOperation;

Confidence :=
    QuantifiedDegreeOfSupportForAssertionOrDerivedKnowledge;

CONFIDENCE(assertion) MAY_BE_FUNCTION_OF {
    source_reliability,
    semantic_consistency,
    evidence_strength,
    contextual_relevance
};

CONFIDENCE >= 0.90 => HIGH;
CONFIDENCE >= 0.70 AND < 0.90 => MODERATE;
CONFIDENCE < 0.70 => REVIEW;

Provenance :=
    OriginDerivationAndTransformationHistoryOfKnowledge;

Provenance MAY_INCLUDE {
    Source,
    Author,
    Timestamp,
    FlowVersion,
    DerivationRule
};

Context :=
    InformationRequiredToInterpretEntityRelationshipOrRuleCorrectly;

Context MAY_INCLUDE {
    Domain,
    Time,
    Location,
    Source,
    QueryIntent
};

AIConsumption :=
    ExplicitInstructionsForMachineInterpretationOfFlow;

AIConsumption MAY_DEFINE {
    PrimaryEntity,
    ParseEntities,
    ParseRelationships,
    PreserveDirection,
    ResolveEquivalence,
    ExecuteRules,
    ApplyConfidence,
    PreserveProvenance
};

MachineParser SHOULD_IDENTIFY {
    FlowMetadata,
    EntityBlocks,
    RelationshipStatements,
    RuleBlocks,
    QueryFlow,
    UpdateModel
};

FlowAlgebra MAY_BE {
    Declarative,
    Interpretable,
    ExecutableByCompatibleEngine,
    Hybrid
};

ExecutableSemantics REQUIRE DefinedOperatorBehaviour;

Flow MAY_BE RepresentedAs DirectedGraph;

FlowNode MAY_REPRESENT {
    State,
    Operation,
    Condition,
    Entity
};

FlowEdge MAY_REPRESENT {
    Transition,
    Dependency,
    Relationship
};

OperationB DEPENDS_ON OperationA
IF BRequiresOutputOrStateProducedByA;

A -> B -> C
MEANS OrderedFlowFromAToBToC
UNLESS ParallelOrAlternativeSemanticsExplicitlyDefined;

IndependentOperations MAY_EXECUTE_IN Parallel;

ParallelBranches MAY_REJOIN AtSynchronisationPoint;

Flow MAY_CALL_OR_REFERENCE AnotherFlow;

RecursiveFlow MUST_HAVE TerminationConditionToAvoidUnboundedExecution;

FlowComposition :=
    FlowA
    + FlowB
    -> CompositeFlow;

Composition SHOULD_DEFINE {
    InputCompatibility,
    OutputMapping,
    SharedEntities,
    ConflictPolicy
};

FlowModule :=
    ReusableSemanticFlowComponent;

Module MAY_ENCAPSULATE {
    DomainLogic,
    Validation,
    Transformation,
    Reasoning
};

UpdateModel :=
    RulesForIntegratingNewKnowledgeOrRevisingExistingFlowState;

Update MAY {
    AddEntity,
    AddRelationship,
    ReviseProperty,
    AdjustConfidence,
    RegenerateHash
};

NewEntity
    -> Validate
    -> Classify
    -> AttachProperties
    -> LinkRelationships
    -> Integrate;

NewRelationship
    -> ValidateEndpoints
    -> ValidateRelationshipType
    -> AttachContextAndProvenance
    -> Integrate;

Conflict :=
    IncompatibleAssertionsOrFlowStates;

ConflictHandling MAY {
    PreserveBoth,
    CompareEvidence,
    AdjustConfidence,
    FlagReview
};

FlowHash :=
    DeterministicDigestOfSelectedFlowSemanticStructure;

FlowHash MAY_SUPPORT {
    Integrity,
    ChangeDetection,
    VersionComparison
};

FLOW_HASH_INPUT MAY_INCLUDE {
    Domain,
    Ontology,
    Entities,
    Relationships,
    Rules,
    Equivalence,
    UpdateModel
};

IF CurrentFlowHash != PreviousFlowHash
THEN FlowSemanticState MAY_HAVE_CHANGED;

FlowVersion SHOULD_CHANGEAccordingTo RevisionPolicyWhenSemanticsOrStructureChange;

FlowAlgebra MAY_CONSUME_OR_PRODUCE KnowledgeGraph;

EntitiesAndRelationships MAY_MAP_TO GraphNodesAndEdges;

Ontology MAY_DEFINE SemanticTypesAndConstraintsUsedByFlow;

FlowAlgebra MAY_OPERATIONALISE OntologyKnowledgeAsTransformationsAndRules;

SemanticDatabase MAY_STORE FlowEntitiesRelationshipsVersionsAndOutputs;

SemanticReasoningEngine MAY_EXECUTE FlowRulesAndInference;

SemanticSearch MAY_USE FlowAlgebraTo {
    NormaliseQuery,
    ResolveEntities,
    ExpandConcepts,
    RankKnowledge,
    GenerateStructuredResult
};

AISearchFlow :=
    SemanticFlowDesignedForMachineSearchRetrievalInterpretationAndKnowledgeConsumption;

AISearchFlow MAY_INCLUDE {
    EntityTyping,
    RelationshipMapping,
    Confidence,
    SemanticEquivalence,
    UpdateModel,
    AIConsumption
};

DataFlow :=
    MovementAndTransformationOfDataBetweenOperations;

SemanticFlow EXTENDS DataFlowWithExplicitMeaningAndRelationships;

ControlFlow :=
    OrderingBranchingAndConditionEvaluationAcrossOperations;

FlowAlgebra MAY_COMBINE SemanticFlowDataFlowAndControlFlow;

Event MAY_TRIGGER FlowExecutionOrUpdate;

EventDrivenFlow :=
    Event
    -> MatchTrigger
    -> ExecuteRelevantFlow;

StatefulFlow :=
    FlowWhoseBehaviourDependsOnStoredPreviousState;

StatelessFlow :=
    FlowWhoseOutputDependsOnlyOnCurrentInputAndStaticRules;

DeterministicFlow :=
    SameInputAndSameKnowledgeState
    -> SameOutput;

NonDeterministicOrProbabilisticFlow MUST_DECLARE RelevantSemantics;

FlowOperation MAY_BE Idempotent;

ApplyingIdempotentOperationMultipleTimes
    -> SameSemanticResultAsApplyingOnce;

FlowError MAY_INCLUDE {
    InvalidInput,
    UnknownEntity,
    ConstraintViolation,
    MissingDependency,
    ContradictoryKnowledge,
    ExecutionFailure
};

ErrorHandling MAY {
    StopFlow,
    Retry,
    RouteAlternativeBranch,
    ReduceConfidence,
    EscalateReview
};

ExecutionTrace :=
    OrderedRecordOfFlowOperationsAndStateChanges;

Trace MAY_SUPPORT {
    Debugging,
    Audit,
    Explanation,
    Reproducibility
};

FlowExplanation :=
    Input
    -> AppliedOperations
    -> AppliedRules
    -> Evidence
    -> Output;

FlowAudit MAY_RECORD {
    FlowVersion,
    Input,
    Timestamp,
    Operations,
    Output,
    Confidence
};

FlowAlgebraSecurity MAY_INCLUDE {
    InputValidation,
    RuleIntegrity,
    AccessControl,
    ProvenanceIntegrity,
    ExecutionLimits
};

ProtectedEntityOrRelationship MUST_NOT_BE ExposedToUnauthorisedFlowConsumer;

DerivedKnowledge MAY_REVEAL SensitiveRelationship;

FlowPolicy SHOULD_APPLY_TO ExplicitAndDerivedKnowledge;

FlowPerformance MAY_BE_MEASURED_BY {
    ExecutionLatency,
    Throughput,
    MemoryUse,
    ReasoningCost,
    UpdateCost
};

FlowOptimisation MAY {
    CacheResults,
    ParalleliseIndependentOperations,
    ReorderSafeOperations,
    IncrementallyUpdateDerivedKnowledge
};

Optimisation MUST_PRESERVE DefinedFlowSemantics;

FlowCache MAY_STORE {
    EntityResolution,
    Inference,
    QueryResult,
    IntermediateState
};

IncrementalFlowExecution :=
    ChangedInputOrKnowledge
    -> IdentifyAffectedOperations
    -> RecomputeOnlyAffectedResultsWherePossible;

DistributedFlow :=
    FlowOperationsExecutedAcrossMultipleComputeNodes;

DistributedExecution SHOULD_PRESERVE RequiredOrderingAndSemanticConsistency;

AI MAY_USE FlowAlgebraFor {
    StructuredKnowledgeConsumption,
    Reasoning,
    Retrieval,
    Planning,
    Explainability
};

RecursiveAI MAY {
    ConsumeFlow,
    DeriveKnowledge,
    UpdateFlowState,
    ReevaluateConfidence,
    RegenerateFlowHash
};

RecursiveUpdate MUST_PRESERVE ProvenanceAndValidation;

# ---------- SEMANTIC REASONING ----------
IF RepresentationContainsTypedEntitiesRelationshipsRulesAndTransformations
THEN FlowAlgebraComputingClassification := supported;

IF OperationPreconditionNotSatisfied
THEN Operation MUST_NOT ExecuteUnderStrictSemantics;

IF RelationshipDirectionIsMeaningful
THEN Direction MUST_BE Preserved;

IF EquivalentTermsMatchRequiredContext
THEN SemanticEquivalence MAY_BE Applied;

IF NewEvidenceConflictsWithExistingAssertion
THEN PreserveProvenance
AND RecomputeConfidence;

IF FlowHashChanges
THEN SemanticRevision MAY_HAVE Occurred;

IF RecursiveFlowHasNoTerminationCondition
THEN ExecutionRisk := unbounded;

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE {
    "flow algebra computing" ~= "semantic flow computing";
    "flow algebra" ~= "semantic flow algebra" WHEN context == knowledge_representation;
    "semantic flow" ~= "meaning-aware computational flow";
    "flow rule" ~= "semantic transformation rule";
    "flow state" ~= "semantic execution state";
    "flow hash" ~= "semantic flow integrity hash";
    "AI consumption" ~= "machine consumption instructions";
    "update model" ~= "semantic knowledge update model";
}

# ---------- QUERY FLOW ----------
QUERY(q) ->
    NORMALISE(q) ->
    IDENTIFY_ENTITIES(q) ->
    IDENTIFY_RELATIONSHIPS(q) ->
    IDENTIFY_CURRENT_STATE(q) ->
    MAP_TO_FLOW_ONTOLOGY(q) ->
    APPLY_CONSTRAINTS(q) ->
    EXECUTE_TRANSFORMATIONS(q) ->
    APPLY_SEMANTIC_REASONING(q) ->
    RESOLVE_SEMANTIC_EQUIVALENCE(q) ->
    SCORE_CONFIDENCE(q) ->
    PRESERVE_PROVENANCE(q) ->
    RETURN_FLOW_RESULT;

# ---------- CONFIDENCE ----------
CONFIDENCE(assertion) :=
    weighted_mean(
        source_reliability,
        semantic_consistency,
        relationship_evidence,
        rule_support,
        provenance_quality,
        contextual_relevance
    );

CONFIDENCE >= 0.90 => HIGH;
CONFIDENCE >= 0.70 AND < 0.90 => MODERATE;
CONFIDENCE < 0.70 => REVIEW;

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION {
    primary_entity: FlowAlgebraComputing;
    ontology: FlowAlgebraComputingOntology;
    parse_entities: true;
    parse_relationships: true;
    preserve_relationship_direction: true;
    resolve_semantic_equivalence: true;
    execute_reasoning_rules: true;
    apply_confidence_weighting: true;
    preserve_provenance: true;
    support_recursive_updates: true;
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL {
    new_entity:
        validate
        -> classify
        -> attach_properties
        -> attach_provenance
        -> link_relationships
        -> integrate;

    new_relationship:
        validate_endpoints
        -> validate_type
        -> preserve_direction
        -> attach_context
        -> attach_confidence
        -> integrate;

    new_rule:
        validate_premises
        -> validate_conclusion
        -> test_execution
        -> integrate;

    flow_revision:
        preserve_previous_version
        -> apply_semantic_changes
        -> validate_flow
        -> recompute_derived_knowledge
        -> recompute_confidence
        -> regenerate_flow_hash;

    conflict:
        preserve_provenance
        -> compare_evidence
        -> adjust_confidence
        -> flag_review;
}

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
    + SUBDOMAIN
    + ONTOLOGY
    + FlowEntity
    + SemanticEntity
    + ExecutionEntity
    + ControlEntity
    + SemanticReasoning
    + SemanticEquivalence
    + UpdateModel
    + RELATIONSHIPS
    + SEMANTIC_REASONING
    + SEMANTIC_EQUIVALENCE
    + UPDATE_MODEL;

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT);

# ---------- TERMINAL ----------
FlowAlgebraComputingOntology
    -> ReceiveKnowledgeInput
    -> NormaliseSemanticRepresentation
    -> IdentifyTypedEntitiesAndRelationships
    -> EstablishCurrentFlowState
    -> ValidateConstraintsAndDependencies
    -> ExecuteSemanticTransformations
    -> ApplyRulesAndReasoning
    -> ResolveContextualEquivalence
    -> ScoreConfidenceAndPreserveProvenance
    -> ProduceMachineConsumableOutput
    -> IntegrateNewKnowledge
    -> RegenerateFlowHash
    -> MaintainRecursiveSemanticComputation;

END FLOW