A homotopy-type-theoretic generalization of neurosymbolic inference
A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $σ$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases. This account is built on sets, and a set deliberately forgets two things that are important for NeSy: when two $σ$-structures are the same up to a symmetry of the theory, and how many distinct proofs witness a query. Types, in the sense of homotopy type theory, preserve this information and turn the functional into a belief-weighted homotopy cardinality, a notion of size that counts each object in inverse proportion to its symmetries. We develop the framewor...
| Authors | Fernando Zhapa-Camacho, Robert Hoehndorf |
|---|---|
| Primary category | cs.AI |
| Published | 16 June 2026 |
| Last updated at source | 31 August 2026 |
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