Current natural language systems designed for multi-step claim validation typically operate in two phases: retrieve a set of relevant premise statements using heuristics (planning), then generate novel conclusions from those statements using a large language model (deduction). The planning step often requires expensive Transformer operations and does not scale to arbitrary numbers of premise statements. In this paper, we investigate whether efficient planning heuristic is possible via embedding spaces compatible with deductive reasoning. Specifically, we evaluate whether embedding spaces exhibit a property we call deductive additivity: the sum of premise statement embeddings should be close to embeddings of conclusions based on those premises. We explore multiple sources of off-the-shelf dense embeddings in addition to fine-tuned embeddings from GPT3 and sparse embeddings from BM25. We study embedding models both intrinsically, evaluating whether the property of deductive additivity holds, and extrinsically, using them to assist planning in natural language proof generation. Lastly, we create a dataset, Single-Step Reasoning Contrast (SSRC), to further probe performance on various reasoning types. Our findings suggest that while standard embedding methods frequently embed conclusions near the sums of their premises, they fall short of being effective heuristics and lack the ability to model certain categories of reasoning.

A growing body of work studies how to answer a question or verify a claim by generating a natural language “proof:” a chain of deductive inferences yielding the answer based on a set of premises. However, these methods can only make sound deductions when they follow from evidence that is given. We propose a new system that can handle the underspecified setting where not all premises are stated at the outset; that is, additional assumptions need to be materialized to prove a claim. By using a natural language generation model to abductively infer a premise given another premise and a conclusion, we can impute missing pieces of evidence needed for the conclusion to be true. Our system searches over two fringes in a bidirectional fashion, interleaving deductive (forward-chaining) and abductive (backward-chaining) generation steps. We sample multiple possible outputs for each step to achieve coverage of the search space, at the same time ensuring correctness by filtering low-quality generations with a round-trip validation procedure. Results on a modified version of the EntailmentBank dataset and a new dataset called Everyday Norms: Why Not? Show that abductive generation with validation can recover premises across in- and out-of-domain settings.

In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but less work has treated the generative version in which a model searches over the space of statements entailed by the premises to constructively derive the hypothesis. We propose a system for doing this kind of deductive reasoning in natural language by decomposing the task into separate steps coordinated by a search procedure, producing a tree of intermediate conclusions that faithfully reflects the system’s reasoning process. Our experiments on the EntailmentBank dataset (Dalvi et al., 2021) demonstrate that the proposed system can successfully prove true statements while rejecting false ones. Moreover, it produces natural language explanations with a 17% absolute higher step validity than those produced by an end-to-end T5 model.

An interpretable system for open-domain reasoning needs to express its reasoning process in a transparent form. Natural language is an attractive representation for this purpose — it is both highly expressive and easy for humans to understand. However, manipulating natural language statements in logically consistent ways is hard: models must cope with variation in how meaning is expressed while remaining precise. In this paper, we describe ParaPattern, a method for building models to generate deductive inferences from diverse natural language inputs without direct human supervision. We train BART-based models (Lewis et al., 2020) to generate the result of applying a particular logical operation to one or more premise statements. Crucially, we develop a largely automated pipeline for constructing suitable training examples from Wikipedia. We evaluate our models using out-of-domain sentence compositions from the QASC (Khot et al., 2020) and EntailmentBank (Dalvi et al., 2021) datasets as well as targeted perturbation sets. Our results show that our models are substantially more accurate and flexible than baseline systems. ParaPattern achieves 85% validity on examples of the ‘substitution’ operation from EntailmentBank without the use of any in-domain training data, matching the performance of a model fine-tuned for EntailmentBank. The full source code for our method is publicly available.