Identifying Implicit Premises for Logical Reconstruction of Argument Graphs

Xuyao Feng; Anthony Hunter

cs.CLAug 19, 2026

Identifying Implicit Premises for Logical Reconstruction of Argument Graphs

Authors: Xuyao Feng, Anthony Hunter

Organizations: Department of Computer Science, University College London, United Kingdom

Abstract

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.

Figures & tables

\begin{array}[]{ll}\mbox{\tt(w / want-01}&\mbox{\tt(w / want-01}\\ \hskip 28.45274pt\mbox{\tt:arg0 (b / boy)}&\hskip 28.45274pt\mbox{\tt:arg0 (b / boy)}\\ \hskip 28.45274pt\mbox{\tt:arg1 (g / go-01}&\hskip 28.45274pt\mbox{\tt:arg1 (g / go-01}\\ \hskip 56.9055pt\mbox{\tt:arg0 b))}&\hskip 56.9055pt\mbox{\tt:arg0 b}\\ &\hskip 56.9055pt\mbox{\tt:polarity -))}\end{array}

Figure 1: AMR for the sentence “The boy wants to go.” (left) and “The boy does not want to go.” (right).

Panel of Figure 2 — Figure 2: Our neuro-symbolic pipeline where the input is a set of natural language sentences (e.g., a premise, implicit premises, and a claim), and the output is a label.

Panel of Figure 3 — Figure 3: Argument graph example (text number 008) where Segment 1 is the central claim. It is directly supported by Segment 2 and Segment 4. Segment 3, in turn, provides support for Segment 4. The claim is challenged by Segment 5, which rebuts it, but this rebuttal is itself undercut by Segments 6 and 7.

Reformatted	Premise: Landfills also produce a lot of odor
Microtext	Claim: Landfills are bad for handling our trash
data	Label: Entailment
Experiment 1	No Implicit Premise
Experiment 2	Single implicit premise: Odor is a negative environmental impact.
Experiment 3	Multi-step chain of implicit premises: (Step 1) Odor indicates poor waste decomposition; (Step 2) Decomposition releases harmful gases; (Step 3) These gases pollute the surrounding air; (Step 4) Air pollution harms human health; (Step 5) Health hazards show inadequate waste management; (Step 6) Inadequate management makes landfills a bad solution.

Table 1: Example of the data format across all three experiments.

Panel of Figure 4 — Figure 4: Results for Experiment 1 (no implicit premises) and Experiment 2 (single implicit premise): Accuracy across different $\tau_{m}$ and $\tau_{c}$ values (solid lines: Experiment 2; dashed lines: Experiment 1). As it is a three-class classification task, random classification would tend to have an accuracy of 0.333.

Panel of Figure 5 — Figure 5: Experiment 3 (using 1 to 5 steps of implicit premises): Precision (prec) and recall (rec) scores for all three classes and overall accuracy across different steps ( $\tau_{m}$ =0.6, $\tau_{c}$ =80).

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Making Implicit Premises Explicit in Logical Understanding of Enthymemes

Xuyao Feng, Anthony Hunter

Department of Computer Science, University College London, United Kingdom

Natural Language Inference Implicit Reasoning in Language Models

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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.

Abstract

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