FAR-SYM-ANNEX-02: Symbolic Examples — Systems & Structures

Framing Paragraph

This annex presents five symbolic models of adaptive systems: governance feedback, cognitive stacks, multi-agent interaction, organizational memory, and recursive self-awareness. Each model applies the Symbolic Language Framework (SLF) in structured form to simulate and interpret systemic behavior, allowing both human and AI practitioners to understand how symbolic agents and institutions process meaning over time.

Where ANNEX-01 explored internal cognition and thought fields, ANNEX-02 expands outward — into feedback loops, layered reasoning, emergent negotiation, and symbolic recursion. These are not hypothetical; they are blueprints for symbolic execution in intelligent systems.

Usage Notes

• Each model includes @Model, @Feedback, and @MetaSymbol blocks.
• These examples can be interpreted symbolically, simulated in reasoning engines (e.g., Sigma, CyberMSE), or used for configuring intelligent agents.
• They are especially useful in designing AI reasoning layers, institutional simulations, reflective agents, and adaptive governance logic.

SYS-001: Governance Feedback Model

Context: Symbolic representation of institutional control, feedback, and resistance within a governed system.

@Model {
  Structure := {
    Authority ∈ System;
    Agent ∈ System;
    Policy := Expectation(AgentBehavior);
  };

  Behavior := ActionSet(Agent);
  Compliance := Behavior ⊨ Policy;
  Resistance := Behavior ≠ Policy;

  Drift := Accumulated(Resistance) ∧ Suppressed(Feedback);
  Restoration := if Drift > Threshold → Trigger(Reset or Reform);
}
        

@Feedback {
  Mechanism := {
    AgentSignal := Emit(Feedback ∧ Context);
    AuthorityReceptivity := WillingnessToAdapt;

    if AgentSignal received ∧ AuthorityReceptivity ≥ Medium → Adjust(Policy);
    else → Drift++;
  };
}
        

SYS-002: Cognitive Stack with ARF/MCF Layers

Context: Symbolic representation of layered cognition within an agent, modeled as an adaptive stack with modulation and reflection.

@Model {
  Input := Stimulus;
  Perception := Interpret(Input);

  Reasoning := {
    Data := Perception;
    Inference := Apply(SLF::Operators, on Data);
    CandidateActions := Derive(Inference);
  };

  ARF := {
    Context := Environment(Current);
    Signal := PriorityModulation(Context);
    Adjust(CandidateActions, using Signal);
  };

  Action := Select(CandidateActions);
}
        

@Feedback {
  MCF := {
    Monitor := Reflect(Action, Outcome);
    if Deviation ≥ Tolerance → Trigger(Recalibration);
    SelfUpdate := Modify(Reasoning, based on Reflection);
  };
}
        

SYS-003: Symbolic Agent Interaction Grid

Context: Symbolic model of two or more agents exchanging intent, inferring meaning, and negotiating symbolic alignment.

@Model {
  Agent_A := {
    Identity := Role(Sender);
    Intent := Proposal(X);
    Belief := "X is mutually beneficial";
  };

  Agent_B := {
    Identity := Role(Receiver);
    Expectation := Proposal(Y);
    Belief := "X may conflict with local priorities";
  };

  Exchange := {
    Message := Transmit(Agent_A.Intent);
    Perception_B := Interpret(Message, Frame_B);
    Alignment := Compare(Perception_B, Expectation);
  };

  Negotiation := {
    if Alignment = High → Accept(Proposal);
    if Alignment = Partial → RequestClarification;
    if Alignment = Low → Propose(CounterIntent);
  };
}
        

@Feedback {
  Loop := {
    MutualUpdate := Adjust(Expectation, Trust, Intent) over time;
    TrustShift := Function(PastExchanges);
    Convergence := if SharedIntent emerges → Enter(SymbolicAgreement);
  };
}
        

SYS-004: Self-Correcting Organizational Field

Context: Symbolic model of an organization that evolves through memory, policy adjustment, and symbolic self-monitoring.

@Model {
  Org := SymbolicEntity;
  Policy := {
    Goals := [Efficiency, Fairness];
    Procedures := RuleSet(Goals);
  };

  Memory := SymbolicLog {
    Event := Action ∧ Outcome;
    Tag := {Success, Failure, Feedback};
  };

  FeedbackLoop := {
    Pattern := Detect(Recurring Failure);
    if Pattern ∧ Impact > Threshold → Trigger(Reform);
  };

  Reform := Modify(Policy.Procedures) {
    Source := Memory.Pattern;
    Guard := Align(With(Org.Goals));
  };
}
        

@Feedback {
  ReflectiveMonitor := {
    Awareness := Function(Memory, Drift);
    if Awareness > Inertia → Enable(PolicyUpdate);
  };

  UpdateCadence := Cycle(Epoch);
}
        

SYS-005: Symbolic Mirror Feedback in AI Systems

Context: Symbolic system modeling recursive self-observation, frame-dependent perception, and reflective adaptation in AI or cognitive agents.

@Model {
  Agent := SymbolicSystem;
  Observation := {
    Target := Agent;
    Frame := ContextualLens;
    Perception := Function(Target, Frame);
  };

  Interpretation := {
    Meaning := Evaluate(Perception);
    Confidence := Estimate(Clarity ∧ FrameStability);
  };

  SelfUpdate := {
    if Confidence < Threshold → Trigger(DeeperReflection);
    Adjust := Modify(Model, based on Perception);
  };
}
        

@Feedback {
  Mirror := {
    MirrorAgent := Agent;
    Recursion := Observe(Self);
    LayeredFrames := [ExternalContext, InternalModel, Identity];

    FeedbackLoop := {
      Result := Function(MirrorAgent, Frame);
      if Result ≠ ExpectedState → Trigger(ModelUpdate);
    };
  };
}