Source-linked AI summary
Identifying Implicit Premises for Logical Reconstruction of Argument Graphs
Xuyao Feng, Anthony Hunter
TL;DR
Reconstructing argument graphs is difficult because natural-language arguments often omit premises needed to connect statements logically. This paper uses an LLM-based neuro-symbolic pipeline to generate and formalize those premises, achieving strong, balanced classification across entailment, contradiction, and neutrality while reconstructing arguments.
Problem
Reconstructing argument graphs is difficult because enthymemes omit premises, and identifying missing premises from common and commonsense knowledge remains challenging.
Method
The pipeline prompts an LLM to generate intermediate implicit premises, then translates them with explicit premises and claims into logical formulas.
Results
The approach achieved strong, balanced performance across entailment, contradiction, and neutrality while also providing logically reconstructed arguments.
Takeaways & Limitations
The pipeline provides a framework for generating implicit premises that make known semantic relations between explicit premises and claims logically explicit.
Takeaways & Limitations
The evaluation does not yet cover end-to-end argument mining directly from plain text, which is reserved for future work.
Abstract
from arXiv · showhide
The logical reconstruction of argument graphs from natural language text is challenging because of the prevalence of enthymemes (i.e., arguments with implicit premises). There are natural language processing methods for identifying enthymemes in text, and there are symbolic methods based on abduction for identifying missing premises in a logical representation of enthymemes. However, there is a need for methods to generate implicit premises to logically show a known entailment or contradiction relationship between a pair of statements. To address this, we propose a neuro-symbolic pipeline that uses large language models (LLMs) to generate intermediate implicit premises that are translated into logical formulae and used with logical formulae representing explicit premises and explicit claims to show the logical relationships between them (entailment, contradiction, or neutrality). Our approach is evaluated on the Microtext Argumentative Corpus.
1. Introduction
Logical reconstruction of argument graphs is hindered by enthymemes and the difficulty of recovering premises from common and commonsense knowledge. This paper proposes an LLM-based neuro-symbolic pipeline that generates implicit premises to establish known entailment or contradiction relationships, evaluated on the Microtext Argumentative Corpus.
- Argument-graph reconstruction formalizes premises and claims as nodes connected by entailment, contradiction, or neutrality edges, but enthymemes make the inferential structure incomplete.The paper identifies enthymemes—arguments with logically implicit premises—as a central challenge for computational argumentation.
- Existing approaches identify enthymemes with natural language processing or recover missing premises logically through abduction, yet common and commonsense knowledge remains difficult to use.Prior methods also address missing premises from dialogue moves, but the paper emphasizes the unresolved challenge of commonsense premise identification.
- The paper builds on prior neuro-symbolic work linking argument mining and symbolic reasoning, including classification of entailment, contradiction, and neutral relationships between formulae.Earlier work translated free-text enthymemes into logic and used sentence embeddings for relationship classification.
- The proposed pipeline prompts an LLM to generate implicit premises that, once translated into logic, establish a known entailment or contradiction between an explicit premise and claim.The task is framed as generating the premise that makes a labeled logical connection explicit, with entailment, contradiction, or neutral relation labels.
- The approach is evaluated on the Microtext Argumentative Corpus, extending the authors’ prior work on implicit-premise generation.The introduction presents the corpus as the dataset used for this paper’s evaluation.
2. Abstract meaning representation
AMR represents sentences as rooted, labelled, directed acyclic graphs and is designed to assign similar graphs to differently worded sentences. The pipeline parses text into AMR graphs, translates them into propositional logic, and uses standard logical connectives for reconstruction.
- AMR represents sentences as rooted, labelled, directed, acyclic graphs, aiming to give similarly worded sentences the same graph.Negation is represented with the :polarity relation.
- The IBM Transition AMR parser loads the pre-trained AMR 3.0 ensemble model to translate each text sentence into an AMR graph.The model combines smatch-based ensembling with ensemble distillation.
- The extended AMR-to-logic converter transforms AMR graphs into propositional formulas by rewriting first-order formulas and grounding existential variables.The extension is based on the Bos algorithm and an open-source Python library.
- The pipeline uses propositional atoms and the connectives negation ¬, conjunction ∧, disjunction ∨, implication →, and biconditional ↔.These formulas follow the usual definitions of propositional logic.
3. Pipeline
The pipeline uses an LLM to generate implicit reasoning steps, translates explicit and implicit statements into logical formulas, relaxes those formulas, and applies automated reasoning. It matches AMR atoms with embeddings and checks contradictions using natural language inference.
- Pipeline components: The pipeline has five components: LLM premise generation, text-to-AMR parsing, AMR-to-propositional-logic translation, formula relaxation, and PySAT reasoning.These components span premise generation, symbolic translation, relaxation methods, and automated logical inference.
- Implicit-premise generation: The LLM receives an explicit premise, claim, and relationship label, then generates either one or six intermediate reasoning steps.The steps form a reasoning chain that makes explicit how the claim follows from or contradicts the premise.
- Logical translation: DeepSeek v3.2-generated implicit premises are parsed into AMR and translated into propositional-logic formulas alongside explicit premises and claims.The resulting formulas use atoms with negation and conjunction, enabling subsequent relaxation and reasoning.
- Formula relaxation: The relaxation process maps AMR atoms to shared propositional letters when their template-based sentence embeddings exceed threshold τm.The pipeline instantiates 29 predicate-specific natural-language templates and compares their embeddings using the BAAI bge-small-en-v1.5 model.
- Matching and contradiction detection: After matching each claim atom to its best premise counterpart, an NLI model classifies the pair as entailment, contradiction, or neutrality using scores sEnt, sCon, and sNeu.The model selects the highest-scoring label, while contradiction checking uses a neuro-contradict threshold τc.
4. Experiments
The experiments evaluate the pipeline on a reformatted Microtext Argumentative Corpus dataset using three-class premise–claim classification. Results compare no implicit-premise generation, single-step generation, and up to five reasoning steps across threshold settings.
- Dataset: The Microtext Argumentative Corpus contains 112 argumentative texts divided into 576 expert-annotated segments with claims, premises, and support or attack relations.The corpus was specifically designed for argument-mining research.
- Dataset: Argument-graph arcs were converted into premise–claim pairs labeled entailment, contradiction, or neutrality using the original corpus relations.Conjunctions of segments were also used for some premise–claim pairs.
- Experimental design: The three experiments tested a baseline without implicit premises, single-step implicit-premise generation, and multi-step generation, while varying neuro-matching and neuro-contradiction thresholds in the first two experiments.The first two experiments varied τm from 0.5 to 0.8 and τc among 80, 90, and 100.
- Results: Lower τc values improved contradiction performance without significantly degrading entailment or neutrality, motivating τm = 0.6 and τc = 80 for Experiment 3.This choice prioritized contradiction and entailment performance while maintaining reasonable overall accuracy.
5. Discussion
The paper introduces a framework for generating implicit premises that logically justify known semantic relations between explicit premises and claims, achieving strong, balanced performance across three classes. Future work will extend the pipeline toward end-to-end logical argument mining from plain text.
- The framework systematically generates implicit premises that make known entailment or contradiction relations between explicit premises and claims logically explicit.It takes a premise–claim pair and its relation label as input.
- The pipeline achieved strong, balanced performance across all three relation classes on a dataset involving substantial implicit reasoning.
- Future work will apply the pipeline to end-to-end logical argument mining by processing plain text and generating logical argument graphs from unstructured text.