3. Mapping Property by Property — From the Human Task to the Cyber-Physical Task

Applying Cognitive Continuum Theory to AI-IoT systems requires careful translation. The eleven task properties proposed in the Hammond tradition were formulated to characterize the conditions that induce more intuitive, more analytical, or mixed modes of cognition. They are not, therefore, stable psychological attributes of the decision-maker; they are properties of the informational, temporal, and structural configuration of the problem that decision-maker faces. The task can induce different modes depending on the cues available, how they are presented, the uncertainty of the criterion, and the time available to act.

In the cyber-physical domain, this distinction requires an additional precaution. The same industrial process can constitute different tasks for different components of the decision chain. The algorithmic policy may receive a dense matrix of time series, derived variables, and signal embeddings; the human supervisor may receive a summarized dashboard, a risk classification, an alert, and a recommendation. One should not, therefore, speak of "the task" as though the AI and the human necessarily faced the same representation of reality.

The classification proposed here consequently distinguishes three levels:

$$\text{Physical Ecology} \rightarrow \text{Representation Available to the AI} \rightarrow \text{Representation Available to the Supervisor}$$

Physical ecology is the real process: equipment, sensors, failure modes, operating conditions, and consequences. The algorithmic representation is the set of signals, transformations, and variables actually accessible to the AI's input-output policy. The supervisory representation is the set of cues presented to the human: dashboard, alert, score, report, explanation, history, or recommendation. The operational problem may be a single one, but the cognitively relevant tasks can diverge across these three levels.

This distinction matters especially for the trilogy. Article 3 classifies the structure of the task; Article 4 will ask what decision architecture is suited to that structure; and Article 5 will audit whether the algorithmic policy and the human policy actually correspond to the environment and to the cues made available to them.

The table below presents the proposed translation of the eleven structural properties for AI-IoT tasks. The intuitive–analytical polarity follows the Hammond tradition: tasks with many cues, high redundancy, low decomposability, low certainty, simultaneous presentation, and a short time window tend toward the intuitive pole; tasks with fewer cues, objective measures, low redundancy, greater decomposability, higher certainty, an available organizing principle, sequential presentation, and more time tend toward the analytical pole. The coexistence of properties pointing in opposite directions is precisely the typical condition of quasirationality.

3.1. Number of Cues: What Counts as a Cue?

The most obvious translation of "number of cues" would be to count sensors. That solution is insufficient. Ten sensors may measure nearly identical variations of the same physical condition; conversely, a single vibration signal can generate dozens or hundreds of informative attributes — energy per frequency band, kurtosis, envelope, harmonics, temporal trend, and anomaly indicators.

The relevant unit is not, therefore, the raw sensor, but the cue effectively available in the task's representation. For the AI, this includes the variables that actually enter the decision pipeline after preprocessing and feature engineering. For the supervisor, it includes only what reaches the dashboard, the alert, or the report. A system can operate over an ecology of many cues, a high-dimensional algorithmic representation, and a human interface of three aggregated indicators.

This distinction prevents a recurring error: concluding that a task is "complex" for the supervisor because the physical process has hundreds of signals, when the dashboard presents only a risk score, a confidence level, and a binary alert. In that case, the human task may be simple in terms of number of cues, yet difficult due to other properties — for example, the opacity of the organizing principle or the uncertainty of the criterion.

3.2. Measurement and Distribution: Signal Quality Is Not Just Sensor Precision

The "cue measurement" property should be operationalized more broadly than a sensor's nominal precision. In AI-IoT, it includes:

• calibration and drift over time;
• resolution and quantization;
• latency and synchronization between sources;
• communication failures;
• missing data;
• firmware changes;
• changes in the sensor's physical position;
• variability introduced by load, environment, or operator.

A temperature reading can be measured with high precision and still become a weak cue if the measurement point shifts, if the machine's load is not observed, or if different operating regimes mix previously distinct distributions.

"Distribution of values" should not be reduced to the simplistic opposition between normal operation and rare events. Rare-tail events are relevant to risk, but rarity, by itself, does not determine a position on the continuum. What matters is whether the observed values produce distinguishable, interpretable states, or whether they vary in a continuous, unstable space, highly dependent on context. Subsequent auditing should record this property as part of the task's ecology, especially because critical cases may be underrepresented in training and validation data.

3.3. Redundancy: A Task Property and Precursor to Collinearity

Redundancy deserves special treatment because it links this article directly to the collinearity problem discussed in Article 5. Temperature, vibration, electrical power, and pressure sensors may all respond, with different delays and sensitivities, to the same mechanical wear process. The task does not gain four independent sources of evidence simply because the dashboard shows four charts.

In CCT, high redundancy shifts the task toward the intuitive pole; less correlated cues favor analysis. In the AI-IoT context, this property should be recorded through empirical metrics — correlation matrices, partial correlations, condition number, variance inflation factors, information redundancy, or dependence between derived attributes — but the metric does not replace engineering interpretation. Two variables may show low correlation in the sample and still be proxies for the same physical mechanism under specific operating regimes.

The conceptual contribution is simple: collinearity should not appear only in Article 5 as a statistical difficulty to be repaired after modeling. It is, before that, a structural property of the task. Article 3 makes it classifiable ex ante; Article 5 will examine the consequences of that structure for estimating weights, matching, and human use of the algorithmic recommendation.

3.4. Decomposability and Organizing Principle

Decomposability asks whether the task can be separated into relatively independent components. A rule such as "temperature above $90^\circ\text{C}$ for more than 15 minutes" describes a decomposable sub-decision. By contrast, identifying incipient degradation from the combination of vibration, load, lubrication, thermal regime, and frequency shifts may be essentially multivariate.

The availability of an organizing principle is different, though related. A task can be poorly decomposable and still have a robust physical model. For example, an engineer may know that a harmonic pattern, under a given load and temperature, corresponds to bearing wear, even though the pattern cannot be reduced to a single threshold. Conversely, a statistical correlation may be highly predictive without offering a physical principle that lets the supervisor understand why they should trust it.

This distinction helps avoid a simplistic opposition between "rules" and "machine learning":

• an engineering-based rule is more defensible when a known organizing principle exists, measures are reliable, and the relationship between signals and criterion is stable;
• statistical or machine-learning models may be appropriate when the task is multivariate, poorly decomposable, or dependent on complex interactions;
• but a statistical model does not automatically make the task analytical, nor does the absence of explanation automatically make it intuitive.

The classification remains one of the task, not of the technology chosen to solve it.

3.5. Certainty, Nonlinearity, and Weighting

Certainty concerns the stability of the relationship between the available evidence and the relevant criterion. A relationship can be physically deterministic in principle and, in practice, uncertain due to partial observation, mixing of regimes, missing data, maintenance changes, or multiple causes producing the same apparent pattern.

The "cue–criterion relationship" property must be delimited with particular care, because it will be revisited in Article 5. Gradual thermal degradation may approximate a linear relationship; catastrophic failures may depend on thresholds, interactions, hysteresis, or abrupt regime transitions. The classic CCT formulation associates linear relationships with the intuitive pole and nonlinear relationships with the analytical pole — a polarity that may seem counterintuitive to readers accustomed to associating formal calculation with linear models. The article should preserve the original polarity, but should not turn this property into a strong causal rule about AI technologies.

In particular, a nonlinear relationship in the physical process does not automatically translate into a high value of $C$ in the Lens Model Equation. $C$ is a residual correlation between components unexplained by the environment's and the judge's linear models; it may reflect shared nonlinear patterns, but also other forms of residual structure. Article 3 classifies the structural possibility of nonlinearity in the task; Article 5 will assess whether observable residual correspondence exists between policy and environment.

Cue weighting asks whether all cues contribute in roughly comparable ways, or whether the decision depends on a few cues with very unequal weight. In the industrial domain, weights may shift by failure mode: vibration may dominate bearing-failure detection, while pressure, temperature, and flow rate may be more relevant to hydraulic degradation. Classification should therefore be done by task and failure mode, not by industrial asset in the abstract.

3.6. Presentation and Duration: Formalizing Temporal Aliasing

The presentation and duration properties establish the most direct link between this article and Article 2. What was there described as the erosion of the ecological validity of supervision through temporal aliasing can now be formulated as a classifiable combination of two CCT properties:

• cue presentation determines whether the supervisor receives simultaneous, fragmented, sequential, summarized, or alert-filtered information;
• decision duration determines whether there is time to inspect context, consult trends, request validation, or review a recommendation before acting.

Duration is not the interval until the failure manifests. It is the window between the moment the decision becomes necessary and the moment an action ceases to have practical, economic, or safe value. A failure may occur only days later yet require a decision within seconds; or it may pose immediate risk while still allowing hours of diagnosis before intervention.

A dashboard that reveals a risk score before the underlying signals, for instance, may shift the human task toward a form of decision anchored by the recommendation. A dashboard that presents trends, operating context, and uncertainty first, and only then the recommendation, may induce a different integration of the same cues. This does not, by itself, demonstrate better performance; it does, however, make the informational structure of supervision observable and classifiable.

Application Rule

To avoid impressionistic classifications, each property should be recorded in a task record with four fields:

The result should not be presented as an objective truth about the task. It is an explicit, revisable, auditable classification. Dhami and Thomson (2012) note precisely that the properties are difficult to decompose in a fully objective way and that CCT does not specify how much each property shifts the cognitive mode. Recent qualitative work applying CCT to risk decisions — for example, Conlon, Raeburn & Wand (2024), on mental health risk assessment by nurses — continues to document exactly this kind of difficulty in practice. Methodological honesty requires that every attribution be justified, and that ambiguous cases remain marked as ambiguous rather than forced toward one pole.

Preliminary Illustration: Argus

Consider, for illustrative purposes, two tasks that might arise within Argus.

The first is thermal anomaly detection in a motor, under a known operating regime. If the decision rests on a few calibrated sensors, with a stable thermal trend, known engineering thresholds, an understandable physical relationship, and enough time to confirm the alert, the task approaches the analytical pole. Even so, it may remain quasirational if motor load, ambient ventilation, and operating cycles alter the interpretation of temperature.

The second is bearing failure prediction from vibration. The task may involve high-frequency signals, derived attributes, strong redundancy between measures, interaction with load and speed, multiple failure modes, and scarcity of positive events. Even if the human interface is reduced to a single score, the ecology and the algorithmic representation may be structurally complex, poorly decomposable, and uncertain. The likely classification is not purely "intuitive" or "analytical," but quasirational: different properties point in opposite directions.

This difference matters for the design that follows. The supervisor should not be expected to mentally reproduce the algorithmic inference for a high-dimensional, poorly decomposable task; but nor should an opaque recommendation be treated as sufficient grounds for action when the interface prevents assessing its contextual validity.

The following section will translate these classifications into an adapted Task Continuum Index. That index will not demonstrate that the human, the AI, or the hybrid system responds in the mode the task induces. It will show only the task's structural position on the continuum. The difference between the mode the task calls for and the policy actually executed by the system is precisely what Article 5 will be able to audit through $G$, $R_s$, cue weights, and the relationship with the criterion.