Related papers: Quantitative Linear Logic for Neuro-Symbolic Learn…

Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed…

Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic…

Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic…

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures…

With the continuous advancement of reasoning abilities in Large Language Models (LLMs), their application to scientific reasoning tasks has gained significant research attention. Current research primarily emphasizes boosting LLMs'…

Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural…

Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a…

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose $\textbf{Additional Logic Training (ALT)}$, which aims to enhance LLMs' reasoning capabilities by…

Ensuring large language model (LLM) reliability requires distinguishing objective unsolvability (inherent contradictions) from subjective capability limitations (tasks exceeding model competence). Current LLMs often conflate these…

Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from…

Current benchmarks for long-context reasoning in Large Language Models (LLMs) often blur critical factors like intrinsic task complexity, distractor interference, and task length. To enable more precise failure analysis, we introduce…

We introduce a framework for learning continuous neural representations of formal specifications by distilling the geometry of their semantics into a latent space. Existing approaches rely either on symbolic kernels -- which preserve…

We study two fundamental questions in neuro-symbolic computing: can deep learning tackle challenging problems in logics end-to-end, and can neural networks learn the semantics of logics. In this work we focus on linear-time temporal logic…

Quantitative reasoning is a critical skill to analyze data, yet the assessment of such ability remains limited. To address this gap, we introduce the Quantitative Reasoning with Data (QRData) benchmark, aiming to evaluate Large Language…

Recent progress in deep reinforcement learning (DRL) can be largely attributed to the use of neural networks. However, this black-box approach fails to explain the learned policy in a human understandable way. To address this challenge and…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…

Discovering governing differential equations from observational data is a fundamental challenge in scientific machine learning. Existing symbolic regression approaches rely primarily on quantitative metrics; however, real-world differential…

Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…