Neural Unification for Logic Reasoning over Natural Language

Abstract

Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where conjectures and axioms are formally provided (e.g. formalised as First Order Logic formulas). Recent approaches, such as , have proposed transformer-based architectures for deriving conjectures given axioms expressed in natural language (English). The conjecture is verified through a binary text classifier, where the transformers model is trained to predict the truth value of a conjecture given the axioms. The RuleTaker approach of (Clark et al., 2020) achieves appealing results both in terms of accuracy and in the ability to generalize, showing that when the model is trained with deep enough queries (at least 3 inference steps), the transformers are able to correctly answer the majority of queries (97.6%) that require up to 5 inference steps. In this work we propose a new architecture, namely the Neural Unifier, and a relative training procedure, which achieves state-of-the-art results in term of generalisation, showing that mimicking a well-known inference procedure, the backward chaining, it is possible to answer deep queries even when the model is trained only on shallow ones. The approach is demonstrated in experiments using a diverse set of benchmark data. The source code is available at this location 1 .

Empirical Investigation of Neural Symbolic Reasoning Strategies

“…The model outputs a single reasoning step per call. Each generated step is concatenated to the past input, and the model again generates the next step (i.e., proofwriter style) (Liang et al, 2021;Sanyal et al, 2022;Picco et al, 2021;Tafjord et al, 2021;Shwartz et al, 2020) . This process is iterated until the model outputs the answer or until a set maximum number of iterations is reached (100).…”

“…Note that this strategy typically derives a long reasoning chain; from an engineering perspective, this strategy is inefficient. Backward chaining: The model starts from the equation for the target variable and backtracks over the dependent equations until it reaches a known value (Picco et al, 2021;Rocktäschel and Riedel, 2017;Cingillioglu and Russo, 2019). Then, it solves each equation in order by inserting known or calculated values until the target one is reached.…”

“…intermediate reasoning step generation (all at once vs. step-by-step vs. token-by-token). Some studies trained the models to generate reasoning steps and a conclusion derived from them at once (Nye et al, 2021;Lewkowycz et al, 2022;Kojima et al, 2022;Recchia, 2021), some generated a single reasoning step given the input and iterated this process until achieving a conclusion (Sanyal et al, 2022;Picco et al, 2021;Tafjord et al, 2021), and others iteratively generated sub-goals as well as reasoning steps (Liang et al, 2021;Shwartz et al, 2020).…”

“…In turn, the chaining strategy ( §2.2) defines the reasoning path direction (shortest path vs. exhaustive path vs. backward path). For example, some studies used a backward chaining process (Picco et al, 2021;Rocktäschel and Riedel, 2017;Cingillioglu and Russo, 2019), while others adopted exhaustive searches (Tafjord et al, 2021;Liang et al, 2021;Yang et al, 2022).…”

Explicit Planning Helps Language Models in Logical Reasoning

“…Our system is a kind of general model programs (Dohan et al, 2022)especially those with verification models (Cobbe et al, 2021)-which use language models inside as probabilistic programs and apply disparate inference algorithms to the models. Other kinds of approaches to use LMs for reasoning include training discriminative models Picco et al, 2021;Ghosal et al, 2022;Zhang et al, 2023), prompting GPT-3 with spelled-out reasoning procedure (Wei et al, 2022;Talmor et al, 2020), and distilling GPT-3.5 (Fu et al, 2023).…”