























Abstract:Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a semantics to interpret them as real-valued functions to be folded in the loss function. A defining trade-off of the field is that between logical properties of the connectives, and analytic concerns for the semantics, with both aspects being relevant in applications. At one extreme we find fuzzy logics, that have well-established algebraic and proof-theoretic foundations, and at the other ad-hoc differentiable logics like Fischer's DL2, conceived for deep learning applications. However, no satisfactory foundation has emerged yet. We propose a resolution to this long-standing tension via a novel logic, Quantitative Linear Logic (QLL), with foundational ambitions. Our design is driven by naturality -- the idea that, since logical constraints are translated to losses, the semantics of the connectives should be pertinent operations used in ML practice (that is, sum and log-sum-exp) on additive quantities (like logits). We then judge the result on two aspects: logical adequacy -- that they satisfy most of the standard logical laws of Linear Logic; and empirical effectiveness -- test-time performance (as measured by adversarial attacks) is well-correlated to the actual verification of the logical constraints (as measured by off-the-shelf neural network verifiers), which makes QLL stand out among SoTA techniques.
| Comments: | 23 pages, 2 figures, 13 tables |
| Subjects: | Logic in Computer Science (cs.LO); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.13845 [cs.LO] |
| (or arXiv:2605.13845v2 [cs.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13845 arXiv-issued DOI via DataCite |
From: Thomas Flinkow [view email]
[v1]
Wed, 13 May 2026 17:59:40 UTC (5,906 KB)
[v2]
Thu, 14 May 2026 17:00:29 UTC (5,901 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。