Making Implicit Premises Explicit in Logical Understanding of Enthymemes

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 knowledge base 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."

Detailed Summary:

The paper addresses the challenge of handling enthymemes—arguments where some premises or claims are implicit—which are common in real-world text and dialogues. The authors identify two major shortcomings in existing research: NLP methods do not decode their underlying logic, while symbolic approaches assume a knowledge base with sufficient formulae but lack a method to generate those formulas from the free-textual components of an enthymeme.

To resolve this, the authors propose a comprehensive neuro-symbolic pipeline that integrates several key components:

1. Generation of Implicit Premises (LLM): The process begins by using a large language model (LLM) to generate intermediate implicit premises. This step uses a specific prompt structure where the LLM is asked to provide two distinct chains of reasoning starting from the premise and finishing with the claim, resulting in both a Helpful Chain (which supports the claim) and a Non-Helpful Chain (which contradicts or is neutral to it).

2. Text-to-AMR Parsing: The natural language sentences—the explicit premise, implicit premises, and claim—are translated into an Abstract Meaning Representation (AMR) graph using the IBM Transition AMR parser.

3. AMR-to-Propositional-Logic Translation: The AMR graph is then converted into a logical formula using the Bos algorithm. This process involves extending an open-source library to transform the first-order logic into a propositional logic formula, referred to as an AMR formula.

4. Relaxation Methods (Neuro-Symbolic Reasoning): The core of the reasoning relies on two relaxation methods:

• Neuro-Matching: This method determines if an AMR atom in a claim is equivalent to an AMR atom in a premise. It involves using word embeddings (specifically, the BAAI general embedding model bge-small-en-v1.5) to calculate the similarity between instantiations of templates derived from the atoms. The neuro-matching relation alpha beta holds if beta is the atom in a premise that maximizes similarity with all other atoms in a claim, provided that similarity exceeds a threshold tau m.

• Neuro-Contradiction (: This method uses a Natural Language Inference (NLI) model to check for conflict. The neuro-contradict relation alpha beta holds if the NLI function N((Inst(alpha, T 1), Inst(beta, T 2)) returns Con (contradiction) with a high score (at least tau c).

5. Translation to Abstract Formulas: The AMR formulas are translated into abstract formulas by applying a mapping function g. This function ensures that atoms identified as being neuro-matched (alpha beta) are mapped to the same propositional letter (g(alpha) = g(beta)), and contradictory atoms (alpha beta) are mapped to complementary literals (g(alpha) = g(beta)).

6. Automated Reasoning (PySAT): Finally, these relaxed abstract formulas are converted into Conjunctive Normal Form (CNF) using SymPY, and then PySAT is used to check for consistency. To prove entailment (phi psi, where phi is the conjunction of the premise and implicit premises), the system checks if phi psi is inconsistent. To prove contradiction, it checks if phi psi is consistent.

Evaluation:

The pipeline was evaluated on two datasets: ARCT (The Argument Reasoning Comprehension Task) and ANLI (The Abductive Natural Language Inference dataset). The authors found that Multi-step implicit premises, especially 3-step ones, yield the highest accuracy at moderate tau m values. Furthermore, the accuracy of the pipeline increased when using generated 1-, 2-, and 3-step premises compared to using only the original dataset premise.

The core innovation presented in this paper addresses a fundamental limitation in current AI systems: the inability to decode and reconstruct the underlying logical structure of arguments that are incomplete or implicit (enthymemes).

By integrating Large Language Models (LLMs) with symbolic logic tools, we transform current NLP models from mere detectors of missing information into deductive reasoners.

The primary improvement is the creation of a Neuro-Symbolic Pipeline that allows AI to transition from vague natural language observations to rigorous logical proof. This system can systematically solve the problem of missing links in real-world argumentation.

What the Improved AI System Can Do:

• Generate Causal Hypotheses (Abductive Reasoning): Given a premise and a claim, the system does not just note that they are disconnected; it actively generates plausible intermediate steps (implicit premises) that logically bridge the gap. It can produce multiple helpful chains of reasoning and contrasting unhelpful chains to test plausibility.

• Perform Semantic Relaxation: The system uses word embeddings (e.g., BGE-small) and Natural Language Inference (NLI) to identify which concepts in the claim are semantically equivalent (about) to concepts in the premise, even if they are expressed using different words or verbs. This allows the AI to simplify complex, messy natural language into manageable Abstract Formulas that retain semantic meaning but discard syntactic noise.

• Determine Entailment and Contradiction: By translating these relaxed abstract formulas into Conjunctive Normal Form (CNF) and feeding them into a SAT solver (PySAT), the the system can definitively determine if a claim is logically entailed by a premise, or if it is directly contradicted by it.

The paper provides specific, repeatable methods to formalize natural language ambiguity, which can be used as an architectural module in any advanced AI reasoning system.

• Resolve Ambiguity via Matching: The system can map a highly specific atom from a claim (e.g., arg0(move, tiger)) to the most likely corresponding atom in a premise (e.g., arg0(walk, tiger)) based on maximum semantic similarity ((similarity)), allowing it to understand that moving and walking are semantically equivalent in context.

• Identify Conflict: The system can detect direct logical conflict by using NLI scores to identify when a premise directly contradicts a claim (e.g., determining that arg0(sleep, tiger) arg0(walk, tiger)).

The improved AI system transitions from pattern matching to deductive proof. It can now:

1. Bridge the Gap: Find the logical path between two pieces of information that are not explicitly connected.

2. Simplify Complexity: Abstract complex natural language into a standardized, simplified logical representation (Abstract Formula).

3. Verify Truth Value: Use automated theorem provers (SAT solvers) to provide objective proof of entailment or contradiction based on the generated and matched premises.