💬 NLP

ConformalNL2LTL: Translating Natural Language Instructions into Temporal Logic Formulas with Conformal Correctness Guarantees

The paper proposes ConformalNL2LTL, a novel method that translates natural language instructions into Linear Temporal Logic formulas with user-defined correctness guarantees by iteratively solving open-vocabulary QA problems using large language models enhanced with conformal prediction to minimize user intervention.

Original authors: David Smith Sundarsingh, Jun Wang, Jyotirmoy V. Deshmukh, Yiannis Kantaros

Published 2026-02-23

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CC BY 4.0

Original authors: David Smith Sundarsingh, Jun Wang, Jyotirmoy V. Deshmukh, Yiannis Kantaros

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the boss of a very smart, very fast robot assistant. You want to give it a complex mission, like: "Go to the kitchen, pick up the red box, but if you see a cat, take a picture first, then put the box in the garage."

The problem is, the robot doesn't speak "English." It speaks a very strict, mathematical language called Linear Temporal Logic (LTL). Think of LTL as the robot's "source code." If you type the code wrong, the robot might crash, ignore the cat, or put the box in the wrong place.

Usually, a human expert has to translate your English sentence into this strict code. This is slow, expensive, and prone to human error.

Recently, scientists tried using AI (Large Language Models) to do this translation automatically. It's like hiring a super-fast translator. But here's the catch: AI is confident, but often wrong. It might translate your sentence into code that looks perfect but actually means something totally different. If the robot follows that wrong code, disaster strikes.

This paper introduces a new system called ConformalNL2LTL. It's like hiring a translator who has a built-in "lie detector" and a "safety net."

Here is how it works, using a simple analogy:

The "Double-Check" Team

Imagine you are building a tower out of blocks, but you can only add one block at a time. You have two expert builders:

The Primary Builder (The AI): This is your main translator. It's fast and usually right.
The Assistant Builder (The Secondary AI): This is a backup expert, just in case the first one is confused.

The "Confidence Meter"

The Primary Builder doesn't just say, "Here is the next block." Instead, it runs a quick internal test. It asks itself: "How sure am I that this block is the right one?"

If it's 100% sure: It places the block. The tower grows.
If it's unsure: It stops. It knows that guessing could collapse the tower.

The "Safety Net" (Conformal Prediction)

This is the magic sauce. The system uses a statistical trick called Conformal Prediction. Think of this as a guarantee.

Before you even start building, you tell the system: "I want to be 99% sure that the final tower is built correctly."

The system then sets up a safety net. If the Primary Builder is unsure, it doesn't just guess. It calls in the Assistant Builder.

Scenario A: The Primary Builder is unsure, but the Assistant Builder agrees with it. Great! They place the block together.
Scenario B: The Primary Builder is unsure, and the Assistant Builder is also unsure (or they disagree). Now, the system knows it's in the "danger zone."

The "Human Boss" Step

If both AI builders are confused, the system stops and asks YOU (the human boss).
"Hey boss, we aren't sure if the next block should be 'Pick up' or 'Put down'. Which one do you want?"

Because the system only asks for help when it is truly unsure, you rarely have to step in. But when you do, you fix the mistake immediately.

The Result

The paper shows that this method is amazing for two reasons:

It keeps its promises: If you ask for 99% accuracy, it delivers 99% accuracy. It won't let a wrong code slip through.
It's polite: It rarely bothers you. In their tests, they achieved 99% accuracy while only asking the human for help less than 0.4% of the time.

Why is this a big deal?

Previous methods were like a student who guesses on a test and hopes for the best. If they get it wrong, the robot crashes.
ConformalNL2LTL is like a student who knows exactly when they don't know the answer. They raise their hand, ask the teacher (the human), and get it right.

This means we can finally give robots complex, natural instructions ("Go to the kitchen, avoid the cat...") and be mathematically guaranteed that the robot will understand us correctly, without needing a human to sit there and check every single line of code. It's the bridge between human language and robot safety.

1. Problem Statement

Context: Linear Temporal Logic (LTL) is a standard formalism for specifying complex robotic missions (e.g., surveillance, coverage) with correctness guarantees. However, manually writing LTL formulas requires significant domain expertise. Natural Language (NL) is a more accessible alternative, but existing methods for translating NL to LTL using Large Language Models (LLMs) lack correctness guarantees. They treat LLM outputs as ground truth, ignoring model uncertainty, which can lead to robot plans that fail to meet the original intent.

Objective: The authors aim to design a probabilistic translation algorithm that converts NL instructions into semantically equivalent LTL formulas with a user-defined success rate (e.g., 99% accuracy) on unseen tasks, while minimizing the need for human intervention.

Formal Problem: Given a translation scenario $\sigma = \{\xi, \mathcal{A}\}$ (where $\xi$ is an NL task and $\mathcal{A}$ is a set of robot skills) sampled from an unknown distribution $\mathcal{D}$ , the goal is to generate an LTL formula $\phi$ such that:
$P_{\sigma \sim \mathcal{D}}(\phi \equiv \xi) \geq 1 - \alpha$
where $\equiv$ denotes semantic equivalence and $\alpha$ is a user-specified error tolerance.

2. Methodology: ConformalNL2LTL

The proposed framework, ConformalNL2LTL, integrates Large Language Models with Conformal Prediction (CP) to quantify uncertainty and ensure statistical guarantees.

A. Iterative QA Formulation

Instead of generating the entire LTL formula in one shot, the translation is framed as a sequence of interdependent Question-Answering (QA) tasks.

At each step $k$ , a prompt $\ell(k)$ is constructed containing the original NL task, the robot's skill set, and the partially built LTL formula.
The LLM is asked to propose the next component: either a temporal/logical operator (e.g., $\diamond$ , $\square$ , $\land$ ) or an Atomic Proposition (AP) grounded in the environment.
The process terminates when a specific ending operator (/) is generated.

B. Uncertainty Quantification via Conformal Prediction

To address the lack of confidence in LLM outputs:

Sampling: The primary LLM ( $\psi_p$ ) is queried $m$ times with the same prompt to generate a set of candidate responses.
Frequency as Confidence: The empirical frequency of each unique response is used as a proxy for model confidence.
Semantic Merging: Semantically similar responses (e.g., "pick up box" vs. "grab box") are merged using a similarity threshold $\zeta$ to aggregate their frequencies.
Prediction Sets: Using CP, a prediction set $C(\ell(k))$ $C (ℓ (k))$ is constructed. This set contains the ground truth response with a probability of at least $1-\alpha$ $1 - α$ .
- If the set is a singleton, the algorithm proceeds.
- If the set is non-singleton (indicating high uncertainty), the algorithm invokes a Help Module.

C. The Help Module (Collaborative Uncertainty Resolution)

To minimize human intervention, the system uses a hierarchical help strategy:

Primary Model: Generates a prediction set. If uncertain, it queries an Auxiliary LLM ( $\psi_{aux}$ ).
Intersection: The prediction sets of the primary and auxiliary models are intersected.
- If the intersection is a singleton, that response is selected.
- If the intersection is non-singleton or empty, a human user is asked to select the correct option from the remaining candidates.
Failure Handling: If the user cannot find the correct option in the set, the translation is declared a failure.

D. Theoretical Guarantees

The authors prove that under standard distributional assumptions (i.i.d. scenarios), the algorithm achieves the user-specified translation success rate ( $1-\alpha$ ). The proof relies on lifting the data to sequences of prompts and defining a Non-Conformity Score (NCS) based on the minimum frequency of the correct response across all steps and both models.

3. Key Contributions

First CP-based NL-to-LTL Translator: The first algorithm to apply Conformal Prediction to NL-to-LTL translation, providing rigorous, user-defined correctness guarantees.
Collaborative LLM Framework: Introduces a novel mechanism where a primary and auxiliary LLM collaborate to resolve uncertainty before involving a human, significantly reducing the "help rate."
Model Agnosticism: The method works with both open-source and closed-source LLMs (e.g., GPT-4o, Deepseek) by relying on sampling frequencies rather than internal logit scores.
Theoretical and Empirical Validation: Provides formal proofs for success rates and extensive experiments showing high accuracy with minimal human intervention.

4. Experimental Results

Experiments were conducted on 1,000 translation scenarios involving mobile manipulation tasks (e.g., "Pick up the red box and place it in storage").

Success Rates: The method achieved empirical success rates matching the user-defined targets (e.g., 99.24% success rate for a target of 99%).
Human Intervention (Help Rate):
- With the Auxiliary LLM: The help rate was extremely low (e.g., 0.378% for 99% target). Only 4% of scenarios required human help at least once.
- Without Auxiliary LLM: The help rate jumped significantly (e.g., 7.43% for 99% target), demonstrating the auxiliary model's effectiveness in reducing uncertainty.
Comparison with Baselines:
- Uncertainty-Agnostic (UA) Baseline: Achieved ~87.4% success but offered no guarantees.
- Existing Tools (Lang2LTL, nl2spec): Achieved lower success rates (53%–82%) and lacked mechanisms to detect when assistance is needed.
- Direct NL-to-Plan (CMAS): Achieved 88% success but lacked the modularity and interpretability of the LTL-based approach.
Out-of-Distribution (OOD) Robustness: Even when tested on tasks with different action spaces and environments (violating CP assumptions), the method maintained reasonable success rates (79.5%–84.5%) with low help rates, though theoretical guarantees no longer strictly hold.

5. Significance

Reliability in Autonomous Systems: This work bridges the gap between the flexibility of natural language and the rigor of formal methods. It allows non-experts to specify complex robot missions with mathematically guaranteed correctness.
Reduced Human-in-the-Loop: By using a secondary LLM to resolve uncertainty, the system drastically reduces the burden on human operators, making it viable for real-world deployment where constant human supervision is impractical.
Modularity: The framework separates translation from planning. The generated LTL formulas can be fed into any existing, sound LTL planner, ensuring the final robot execution is correct with respect to the translated specification.

In summary, ConformalNL2LTL represents a significant advancement in AI-enabled robotics by providing a statistically sound, automated pipeline for translating human intent into formal robot specifications, balancing high accuracy with minimal human oversight.