Answer Set Networks: Casting Answer Set Programming into Deep Learning

TL;DR

This paper introduces Answer Set Networks (ASN), a neural-symbolic system based on Graph Neural Networks that efficiently translates and solves Answer Set Programming problems, enabling scalable deep probabilistic logic programming and guiding LLM fine-tuning.

Contribution

The paper presents ASN as a novel GNN-based NeSy solver for ASP, demonstrating its scalability, efficiency, and novel applications like LLM fine-tuning and drone navigation.

Findings

ASNs outperform CPU-bound NeSy systems on multiple tasks.

First demonstration of LLM fine-tuning guided by ASP-based logic.

Encoding of aviation laws in ASN enables autonomous drone routing.

Abstract

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.