💬 NLP

Derivation Prompting: A Logic-Based Method for Improving Retrieval-Augmented Generation

This paper introduces Derivation Prompting, a novel logic-based prompting technique for Retrieval-Augmented Generation that constructs interpretable derivation trees to systematically reduce hallucinations and erroneous reasoning in knowledge-intensive tasks.

Original authors: Ignacio Sastre, Guillermo Moncecchi, Aiala Rosá

Published 2026-05-15

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CC BY 4.0

Original authors: Ignacio Sastre, Guillermo Moncecchi, Aiala Rosá

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 have a very smart, well-read librarian (the AI) who is great at answering questions but sometimes makes things up or gets confused when the answer isn't immediately obvious. This is a common problem with current AI models, especially when they are asked to answer specific questions based on a pile of documents.

This paper introduces a new way to talk to this librarian called Derivation Prompting. Instead of just asking, "What is the answer?" and hoping for the best, the authors teach the librarian to build the answer step-by-step, like solving a puzzle or proving a math problem.

Here is how it works, broken down into simple concepts:

1. The Problem: The "Hallucinating" Librarian

Usually, when you ask an AI a question, it grabs a few relevant pages from a book and tries to write an answer immediately. Sometimes, it gets it right. But often, it might "hallucinate"—meaning it confidently states something that isn't actually in the book, or it mixes up facts. It's like a student who guesses the answer on a test because they think they know it, rather than looking at the textbook.

2. The Solution: Building a "Logic Tree"

The authors suggest a new method inspired by logic proofs. Imagine you are building a tree.

The Roots: These are the facts you found in the documents (the "hypotheses").
The Branches: These are the steps you take to connect those facts.
The Fruit: This is the final answer.

Instead of jumping straight to the fruit, the AI is forced to grow the branches first. It has to follow a specific set of rules (like a recipe) to combine the facts.

3. The Rules: The AI's "Toolbox"

The paper defines a small set of "moves" the AI can make, similar to moves in a board game. For example:

Extract: "Take this specific sentence from the document."
Combine: "Take Fact A and Fact B and put them together."
Refine: "Reword this fact to fit the question better, but don't change the meaning."
NoInfo: "If none of the facts help, admit that you don't know."

The AI must pick a rule, apply it to the facts, and write down the result. Then, it looks at that result and decides: "Is this the final answer? If not, I need to use another rule on this new result."

4. Why This Helps: The "Construction Site" Analogy

Think of a normal AI answer like a contractor who just throws up a wall and hopes it stands. If the wall is crooked, you don't know why until it falls.

Derivation Prompting is like a contractor who has to show you the blueprints and the step-by-step construction log.

Interpretability: Because the AI builds a "tree" of steps, you can look at the middle branches and say, "Wait, you combined these two facts wrong," or "You made up a fact here." It's much easier to spot the mistake because the path is visible.
Control: By forcing the AI to follow rules, it's less likely to wander off and make things up. It's like giving the AI a strict checklist; it can't skip steps or invent new ones.

5. What They Found

The authors tested this on a real-world problem: answering student questions about university administrative rules. They compared three methods:

Long Context: Giving the AI the whole book at once.
Standard RAG: The usual method of grabbing a few pages and answering.
Derivation Prompting: The new step-by-step rule method.

The Results:

The new method significantly reduced "bad" answers (answers that were wrong or made things up).
It didn't necessarily make the AI faster at finding the right answer, but it made the answers it did give much more reliable.
It worked best with a very smart AI model (Claude Opus). A smaller, less powerful model (Claude Haiku) could follow the rules but sometimes got stuck or produced fewer high-quality answers, showing that the AI needs to be "smart enough" to follow the logic instructions.

The Bottom Line

This paper proposes a way to stop AI from guessing by forcing it to "show its work" using a logical, rule-based tree structure. It turns the AI from a confident guesser into a careful, step-by-step problem solver, making it much safer to use for important, fact-based questions.

Technical Summary: Derivation Prompting for Retrieval-Augmented Generation

Problem Statement
While Large Language Models (LLMs) have advanced Question Answering (QA), they remain prone to hallucinations and erroneous reasoning, particularly in knowledge-intensive, domain-specific tasks. The Retrieval-Augmented Generation (RAG) framework attempts to mitigate this by grounding model generation in retrieved documents. However, existing reasoning enhancement techniques, such as Chain-of-Thought (CoT) and Tree of Thoughts (ToT), lack explicit constraints on how intermediate reasoning steps are constructed. This absence of systematic methodology allows models to generate uncontrolled reasoning paths, leading to faulty logic and hallucinations even when context is provided.

Methodology: Derivation Prompting
The authors propose Derivation Prompting, a novel technique for the generation step of the RAG framework, inspired by logical derivations in propositional logic. Instead of generating a free-form answer, the method constructs a structured "derivation tree" where a conclusion is systematically inferred from a set of initial hypotheses (retrieved document chunks) using predefined rules.

Core Mechanism: The process treats retrieved chunks as a set of hypotheses $\{h_1, \dots, h_n\}$ . The LLM is tasked with applying a set of natural language rules to transform or combine these hypotheses to derive a conclusion $c$ that answers the query $q$ .
Rule Set: The method utilizes a specific set of rules defined in natural language, including:
- Extract: Isolating a specific part of a hypothesis.
- Concat: Combining independent hypotheses.
- Instantiate: Generalizing a hypothesis to a particular case.
- Compose: Merging hypotheses sharing a common element.
- Refine: Adapting a hypothesis to fit the query without altering semantics.
- NoInfo: Explicitly stating when hypotheses lack necessary information.
Algorithmic Execution: The process is iterative. The LLM decides which rule to apply, selects the relevant hypotheses, and generates a new conclusion. If the conclusion is not the final answer, it is added to the hypothesis list for subsequent steps.
Implementation Strategies: The authors evaluated two implementation approaches:
1. One-step prompt: Isolating each rule application as an independent LLM call.
2. Whole derivation prompt: Using a Few-Shot strategy to guide the LLM in constructing the entire derivation tree in a single inference call.
  The study found the Whole derivation prompt to be significantly more computationally efficient (replacing $n$ inferences with one) while yielding comparable results.

Case Study and Evaluation
The method was evaluated in a specific domain: administrative information for the School of Engineering at Universidad de la República (Uruguay).

Dataset: 135 real user queries derived from historical emails, processed to remove personal data.
Baselines: The study compared Derivation Prompting against:
- Standard RAG (using Cross-Encoder for retrieval).
- Long-context window approaches (feeding full documents directly to the model).
Models: Experiments utilized Anthropic's Claude 3 family (Haiku and Opus).
Evaluation Metric: An automated evaluation using Claude Opus as a judge, scoring answers on a 1–5 scale based on a rubric distinguishing between "unacceptable" (contradictory/false, scores 1–2) and "acceptable" (non-contradictory, scores 3–5).

Results
The experiments demonstrated that Derivation Prompting significantly improves the precision of RAG systems:

Reduction in Unacceptable Answers: Derivation Prompting with Claude Opus achieved 89.6% acceptable answers, compared to 77.8% for standard RAG and 76.3% for Long Context methods. This represents a substantial reduction in hallucinations and contradictory information.
Precision vs. Recall: While the method drastically reduced errors (scores 1 and 2), it did not necessarily increase the number of highly detailed answers (scores 4 and 5). In many cases where other methods failed with hallucinations, Derivation Prompting correctly identified a lack of information (score 3) via the NoInfo rule.
Model Dependency: The effectiveness of the method is correlated with model capability. While Claude Opus performed robustly, the smaller Claude Haiku model showed a decrease in high-quality answers (scores 4 and 5) despite reducing errors, suggesting that constructing valid derivations requires significant model capacity.
Interpretability: A key finding is that the derivation tree is interpretable. When errors do occur, they can be traced to specific rule applications (e.g., a hallucination during a Refine step), allowing users to identify faulty reasoning rather than just receiving a wrong answer.

Significance and Claims
The paper claims that Derivation Prompting offers a controlled, interpretable alternative to existing reasoning techniques. By forcing the generation process through a sequence of predefined logical rules, the method constrains the model's freedom to hallucinate, ensuring answers remain grounded in the retrieved documents. The authors emphasize that while the method improves precision and reduces unacceptable outputs, its success is contingent on the underlying LLM's ability to understand and apply the rule-based logic effectively. The work suggests that this logic-based approach can be generalized to other RAG scenarios and potentially non-RAG tasks, provided appropriate rule sets are defined.