When Temperature Rises, Who’s to Blame? — Causation in Hybrid Worlds

Opening — Why This Matters Now

Autonomous systems no longer live in neat, step-by-step worlds.

A robot moves through space (continuous change), while its controller switches modes (discrete change). A smart grid reacts to faults (discrete events), while voltage and temperature drift in real time (continuous dynamics). A medical device triggers an alarm (discrete), while a patient’s vitals evolve (continuous).

When something goes wrong — overheating cores, crashing drones, cascading failures — regulators and engineers ask the same question: what actually caused this?

The latest research on primary cause in hybrid dynamic domains confronts this problem head-on. It moves beyond textbook causality models and enters the messy territory where logic meets physics.

And for businesses deploying AI in real environments, this is not philosophical indulgence. It is auditability, liability, and system assurance.

Background — From Counterfactuals to Hybrid Action Theories

Traditional formal accounts of actual causation — especially those inspired by structural equation models (SEM) — work well in discrete domains. You flip a switch, a light turns on. Remove the switch action, and the light stays off. Simple.

But the world is rarely that polite.

Hybrid systems combine:

In such systems:

• An action may enable a context.
• The effect may occur only after time passes.
• Other irrelevant actions may occur in between.

The paper builds on the Hybrid Temporal Situation Calculus (HTSC) — an action-theoretic logic framework that integrates:

• Named actions
• Situations (histories of actions)
• Temporal fluents (values evolving over time)
• Context-sensitive state evolution

This matters because it lets us model systems like nuclear plants, autonomous vehicles, and industrial control systems without flattening them into purely discrete abstractions.

Analysis — What Is a Primary Cause in a Hybrid World?

The core contribution is deceptively sharp:

A primary cause of a temporal effect is the unique action that enabled the context under which the effect was achieved and persisted.

Let’s unpack that.

Step 1: Identify the Achievement Situation

An effect like:

$$ \text{coreTemp}(P1) \ge 1000 $$

is not achieved instantly. It becomes true at a specific situation and remains true afterward.

The authors define an achievement situation as the earliest point in the scenario where:

• The effect becomes true
• It remains true in all later situations

This ensures we are not confusing transient spikes with genuine achievements.

Step 2: Identify the Active Context

Continuous change depends on discrete contexts.

In the nuclear example:

Only one context can be active at a time (mutual exclusivity).

Thus, when temperature crosses 1000°C, the system must be operating under one specific context.

Step 3: Find the Action That Enabled That Context

The primary cause is:

• The action that directly caused the active context
• In the achievement situation
• With no later action falsifying the effect

Crucially:

• Measuring radiation does not count.
• Earlier partial contributors do not count.
• Only the unique action that enabled the decisive context qualifies.

The result is strong:

Primary causes of primitive temporal effects are unique.

That is rare clarity in causation theory.

A Second Route — Causation via Contribution

The paper then takes a more production-oriented route.

Instead of defining causation directly, it defines:

1. Direct possible contributors
2. Direct actual contributors
3. Primary cause as a maximal contributor

This reframes causation as a contribution relation rather than a purely structural trigger.

The surprising result:

The foundational definition and the contribution-based definition are equivalent.

This equivalence matters. It bridges two philosophical camps:

• Structural/achievement-based causation
• Production/contribution-based causation

In practice, it means engineers can reason either from enabling contexts or from contribution chains — and obtain the same answer.

The Modified But-For Test — Fixing Counterfactual Fragility

Classic counterfactual reasoning says:

If removing the cause removes the effect, then it is a cause.

But this fails under preemption.

In hybrid systems, removing one action might allow another previously suppressed context to produce the same effect.

The paper introduces a refined mechanism:

1. Remove the primary cause (replace with noOp).
2. If another primary cause emerges, remove that too.
3. Continue until no primary cause remains.
4. Evaluate the resulting “defused” scenario.

The theorem shows:

In the defused situation, either the effect disappears or the scenario becomes non-executable — provided no relevant context was active initially.

This restores counterfactual dependence without naive simplifications.

Findings — What We Now Know

1. Uniqueness Guarantees

This dramatically reduces ambiguity in hybrid forensic reasoning.

2. Persistence Property

If an action is a primary cause at time $t$ and the effect persists, then it remains the primary cause in all future extensions of the scenario.

For safety audits, this is critical: causation is stable across time.

3. Implicit Causes May Not Exist

If a context was already active from the initial state, no primary cause may exist at all.

This is subtle — and legally relevant. Not every effect has an actionable cause.

Business & Governance Implications

1. Safety-Critical AI

Autonomous drones, medical devices, and industrial robots require causal traceability across discrete decisions and continuous evolution.

This framework enables:

• Formal root cause analysis
• Clear accountability assignment
• Robust audit trails

2. Regulatory Assurance

Emerging AI governance frameworks increasingly demand explainability beyond surface-level attribution.

Hybrid causal semantics supports:

• Counterfactual validation
• Responsibility isolation
• Preemption handling

This is significantly stronger than post-hoc feature attribution.

3. System Design

Designers can structure hybrid systems so that:

• Contexts are mutually exclusive
• Continuous evolution is explicitly modeled
• Causal responsibility is provably unique

That is architecture as governance.

Conclusion — Causation Grows Up

Causation in discrete toy models is comfortable. Hybrid reality is not.

This work shows that:

• Causation can be formally defined in systems combining actions and time.
• Foundational and production-based definitions can converge.
• A refined counterfactual test can survive preemption.

In short: we can reason about who caused what — even when temperature rises gradually and decisions unfold in layers.

For organizations deploying real-world AI systems, that clarity is not academic elegance.

It is operational necessity.

Cognaptus: Automate the Present, Incubate the Future.