# Differentiable Fuzzy ALC: A Neural-Symbolic Representation Language for Symbol Grounding

arXiv: https://arxiv.org/abs/2211.12006 · HTML: https://mlsanity.com/paper/2211.12006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 34 of its 72 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 34)

- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Detect What You Can: Detecting and Representing Objects using Holistic Models and Body Parts](https://mlsanity.com/paper/1406.2031/) (2014)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision](https://mlsanity.com/paper/1611.00020/) (2016)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [Embedding Symbolic Knowledge into Deep Networks](https://mlsanity.com/paper/1909.01161/) (2019)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [Techniques for Symbol Grounding with SATNet](https://mlsanity.com/paper/2106.11072/) (2021)
- [A Boxology of Design Patterns for Hybrid Learning and Reasoning Systems](https://mlsanity.com/paper/1905.12389/) (2019)
- [Onto2Vec: joint vector-based representation of biological entities and their ontology-based annotations](https://mlsanity.com/paper/1802.00864/) (2018)
- [Neuro-symbolic Architectures for Context Understanding](https://mlsanity.com/paper/2003.04707/) (2020)

## Built on by (most cited first, 1 of 1)

- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)

## Abstract (arXiv)

Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, so as to leverage the complementary strengths of both of these, seemingly unrelated (maybe even contradictory) AI paradigms. The central challenge in neural-symbolic computing is to unify the formulation of neural learning and symbolic reasoning into a single framework with common semantics, that is, to seek a joint representation between a neural model and a logical theory that can support the basic grounding learned by the neural model and also stick to the semantics of the logical theory. In this paper, we propose differentiable fuzzy ALC (DF-ALC) for this role, as a neural-symbolic representation language with the desired semantics. DF-ALC unifies the description logic ALC and neural models for symbol grounding; in particular, it infuses an ALC knowledge base into neural models through differentiable concept and role embeddings. We define a hierarchical loss to the constraint that the grounding learned by neural models must be semantically consistent with ALC knowledge bases. And we find that capturing the semantics in grounding solely by maximizing satisfiability cannot revise grounding rationally. We further define a rule-based loss for DF adapting to symbol grounding problems. The experiment results show that DF-ALC with rule-based loss can improve the performance of image object detectors in an unsupervised learning way, even in low-resource situations.