Concretized Proposition Prompting Resolves Composition-Knowledge Dichotomy in Large Language Models

Large Language Models (LLMs) often struggle with a trade-off between compositionality (the ability to structure logical reasoning) and knowledgeability (the ability to retrieve and apply factual information). This paper addresses this 'Composition-Knowledge Dichotomy,' where composition-focused methods often hallucinate due to lack of evidence, and knowledge-focused methods fail due to erratic logical deduction.

The authors propose Concretized Proposition Prompting (CPP), a framework that forces the model to decompose questions into four specific categories of propositions: True Positives (affirming facts), True Negatives (negating fallacies), False Positives (affirming fallacies), and False Negatives (negating facts). The framework operates in three stages:

1. Proposition Generation: A model generates concrete propositions relevant to the question across the four categories.
2. Rationale & Answer Generation: These propositions are provided as context to an answer model to guide its step-by-step reasoning.
3. Prompt Optimization: Using the DSPy framework, the prompts are jointly optimized to maximize a reward function that balances proposition quality (judged by an LLM) and final answer accuracy.

CPP consistently outperforms or remains competitive with existing prompting methods across eight datasets spanning commonsense, math, and medical domains. The study demonstrates that the inclusion of all four proposition categories (TP/TN/FP/FN) is optimal for performance. Furthermore, the method is shown to be scalable across various foundation models (e.g., Llama, Qwen, Gemma) and parameter sizes (7B to 72B), effectively bridging the gap between structure-oriented and knowledge-oriented reasoning paradigms.

This work provides a systematic way to ground LLM reasoning in verifiable propositions. By explicitly categorizing the truth value and logical mode of statements, CPP reduces the risk of 'exquisite hallucination'—where models generate logically sound but factually incorrect rationales—making LLMs more reliable for high-stakes domains like medicine.