Making Implicit Premises Explicit in Logical Understanding of Enthymemes

2026-03-06

AI Summary

This work addresses the challenge of reconstructing enthymematic syllogisms in real-world texts, where premises are often implicit and difficult for current NLP systems to uncover. Traditional logical approaches rely on complete knowledge bases and lack mechanisms for automatic translation from natural language to formal logic. To overcome these limitations, the paper proposes the first end-to-end neuro-symbolic framework that integrates a large language model (LLM) with a SAT solver–based reasoner. The LLM generates plausible implicit premises, which are then automatically translated into logical formulas; symbolic reasoning subsequently verifies the entailment relation. Notably, the method operates without a pre-defined knowledge base and achieves state-of-the-art performance in implicit premise identification, demonstrating strong results across precision, recall, F1 score, and accuracy on two standard benchmarks.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Real-world arguments in text and dialogues are normally enthymemes (i.e. some of their premises and/or claims are implicit). Natural language processing (NLP) methods for handling enthymemes can potentially identify enthymemes in text but they do not decode their underlying logic, whereas logic-based approaches for handling them assume a knowledgebase with sufficient formulae that can be used to decode them via abduction. There is therefore a lack of a systematic method for translating textual components of an enthymeme into a logical argument and generating the logical formulae required for their decoding, and thereby showing logical entailment. To address this, we propose a pipeline that integrates: (1) a large language model (LLM) to generate intermediate implicit premises based on the explicit premise and claim; (2) another LLM to translate the natural language into logical formulas; and (3) a neuro-symbolic reasoner based on a SAT solver to determine entailment. We evaluate our pipeline on two enthymeme datasets, demonstrating promising performance in selecting the correct implicit premise, as measured by precision, recall, F1-score, and accuracy.

Problem

• enthymeme
• implicit premise
• logical entailment
• natural language processing
• logical reasoning

Innovation

• enthymeme
• large language model
• neuro-symbolic reasoning
• logical entailment
• implicit premise generation