# On a Convex Logic Fragment for Learning and Reasoning

arXiv: https://arxiv.org/abs/1809.06778 · HTML: https://mlsanity.com/paper/1809.06778/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2018.

## Built on by (most cited first, 6 of 6)

- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsal](https://mlsanity.com/paper/2302.01242/) (2023)
- [Refining neural network predictions using background knowledge](https://mlsanity.com/paper/2206.04976/) (2022)
- [Semantic Loss Functions for Neuro-Symbolic Structured Prediction](https://mlsanity.com/paper/2405.07387/) (2024)

## Abstract (arXiv)

In this paper we introduce the convex fragment of Lukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any learning framework involving logical constraints. The method is of particular interest since the fragment guarantees to deal with convex constraints, which are shown to be equivalent to a set of linear constraints. Within this framework, we are able to formulate learning with kernel machines as well as collective classification as a quadratic programming problem.