How (and when) can you fit examples to logic-based hypothesis classes over infinite structures?
arXiv:2606.01107v1 Announce Type: cross Abstract: We study fitting problems, sometimes called ``training problems'', where we have a finite sample consisting of inputs and outputs, and we want to know whether there is a function in a certain class that could produce these outputs, exactly or approximately, on the given inputs. We focus on the computational and descriptive complexity of fitting for logically-defined classes in common decidable structures, like the real ordered field and Presburger arithmetic, and also for broader classes defined via combinatorial or model-theoretic properties.
This paper explores fundamental theoretical limits and capabilities of symbolic AI, which is regaining attention amid challenges with purely statistical approaches in achieving robust explainability and generalizability.
Understanding the computational and descriptive complexity of logical hypothesis classes is crucial for developing more reliable and interpretable AI systems, impacting fields like autonomous agents and formal verification.
The research pushes the boundaries of where logic-based AI can effectively 'fit' examples, potentially informing the design of next-generation machine learning algorithms that integrate symbolic reasoning.
- · AI researchers (symbolic AI)
- · Formal verification sector
- · Developers of explainable AI
- · AI systems lacking interpretability
- · Brute-force statistical learning methods
Improved understanding of the theoretical underpinnings for learning logical rules from data.
Development of more robust and auditable AI models for high-stakes applications.
A potential resurgence in hybrid AI approaches combining neural and symbolic methods for greater transparency and generalizability.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG