Coupling Large Language Models with Logic Programming for Robust and General Reasoning from Text

While large language models (LLMs), such as GPT-3, appear to be robust and general, their reasoning ability is not at a level to compete with the best models trained for specific natural language reasoning problems. In this study, we observe that a large language model can serve as a highly effective few-shot semantic parser. It can convert natural language sentences into a logical form that serves as input for answer set programs, a logic-based declarative knowledge representation formalism. The combination results in a robust and general system that can handle multiple question-answering tasks without requiring retraining for each new task. It only needs a few examples to guide the LLM's adaptation to a specific task, along with reusable ASP knowledge modules that can be applied to multiple tasks. We demonstrate that this method achieves state-of-the-art performance on several NLP benchmarks, including bAbI, StepGame, CLUTRR, and gSCAN. Additionally, it successfully tackles robot planning tasks that an LLM alone fails to solve.

Leveraging Large Language Models to Generate Answer Set Programs

Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning capabilities are limited and relatively shallow, despite the application of various prompting techniques. In contrast, formal logic is adept at handling complex reasoning, but translating natural language descriptions into formal logic is a challenging task that non-experts struggle with. This paper proposes a neuro-symbolic method that combines the strengths of large language models and answer set programming. Specifically, we employ an LLM to transform natural language descriptions of logic puzzles into answer set programs. We carefully design prompts for an LLM to convert natural language descriptions into answer set programs in a step by step manner. Surprisingly, with just a few in-context learning examples, LLMs can generate reasonably complex answer set programs. The majority of errors made are relatively simple and can be easily corrected by humans, thus enabling LLMs to effectively assist in the creation of answer set programs.

Causal Laws and Multi-Valued Fluents

This paper continues the line of work on representing properties of actions in nonmonotonic formalisms that stresses the distinction between being "true" and being "caused", as in the system of causal logic introduced by McCain and Turner and in the action language C proposed by Giunchiglia and Lifschitz. The only fluents directly representable in language C+ are truth-valued fluents, which is often inconvenient. We show that both causal logic and language C can be extended to allow values from arbitrary nonempty sets. Our extension of language C, called C+, also makes it possible to describe actions in terms of their attributes, which is important from the perspective of elaboration tolerance. We describe an embedding of C+ in causal theories with multi-valued constants, relate C+ to Pednault's action language ADL, and show how multi-valued constants can be eliminated in favor of Boolean constants.

Elementary Sets for Logic Programs

By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the Lin-Zhao theorem remains correct even if we restrict loop formulas to a special class of loops called ``elementary loops.'' In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop for nondisjunctive programs, but is simpler, and, unlike elementary loops, can be extended to disjunctive programs without producing unintuitive results. We show that the maximal unfounded elementary sets for the ``relevant'' part of a program are exactly the minimal sets among the nonempty unfounded sets. We also present a graph-theoretic characterization of elementary sets for nondisjunctive programs, which is simpler than the one proposed in (Gebser & Schaub 2005). Unlike the case of nondisjunctive programs, we show that the problem of deciding an elementary set is coNP-complete for disjunctive programs.

NeurASP: Embracing Neural Networks into Answer Set Programming

We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can be used to train a neural network better by training with ASP rules so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.

On Loop Formulas with Variables

Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary first-order sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in first-order logic, providing a way to apply first-order theorem provers to reasoning about non-Herbrand stable models.

Safe Formulas in the General Theory of Stable Models

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding -- to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that the stable models of a safe sentence can be characterized by a formula of a simple syntactic form.

Learning to Solve Constraint Satisfaction Problems with Recurrent Transformer

Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner, having clear advantages over state-of-the-art methods such as Graph Neural Networks, SATNet, and some neuro-symbolic models. With the ability of Transformer to handle visual input, the proposed Recurrent Transformer can straightforwardly be applied to visual constraint reasoning problems while successfully addressing the symbol grounding problem. We also show how to leverage deductive knowledge of discrete constraints in the Transformer's inductive learning to achieve sample-efficient learning and semi-supervised learning for CSPs.

Injecting Logical Constraints into Neural Networks via Straight-Through Estimators

Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning. More specifically, we design a systematic way to represent discrete logical constraints as a loss function; minimizing this loss using gradient descent via a straight-through-estimator updates the neural network's weights in the direction that the binarized outputs satisfy the logical constraints. The experimental results show that by leveraging GPUs and batch training, this method scales significantly better than existing neuro-symbolic methods that require heavy symbolic computation for computing gradients. Also, we demonstrate that our method applies to different types of neural networks, such as MLP, CNN, and GNN, making them learn with no or fewer labeled data by learning directly from known constraints.

Learning Missing Modal Electronic Health Records with Unified Multi-modal Data Embedding and Modality-Aware Attention

Electronic Health Record (EHR) provides abundant information through various modalities. However, learning multi-modal EHR is currently facing two major challenges, namely, 1) data embedding and 2) cases with missing modality. A lack of shared embedding function across modalities can discard the temporal relationship between different EHR modalities. On the other hand, most EHR studies are limited to relying only on EHR Times-series, and therefore, missing modality in EHR has not been well-explored. Therefore, in this study, we introduce a Unified Multi-modal Set Embedding (UMSE) and Modality-Aware Attention (MAA) with Skip Bottleneck (SB). UMSE treats all EHR modalities without a separate imputation module or error-prone carry-forward, whereas MAA with SB learns missing modal EHR with effective modality-aware attention. Our model outperforms other baseline models in mortality, vasopressor need, and intubation need prediction with the MIMIC-IV dataset.