Structure-Preserving Uncertainty Propagation in First-Order Proof Search
A recent paper available on arXiv (2608.09190) presents a method for structure-preserving quantitative reporting within GK, a first-order prover designed for query-directed tasks. GK enhances resolution-based proof searching by incorporating explicit positive and negative assertions, numerical confidence metrics, and prioritized default rules with exceptions. It directly processes non-ground clauses, including equality and function terms, using bounded first-order proof searches to identify potential proofs. Exception conditions for defaults undergo recursive checks through additional bounded searches. This method eliminates the necessity for a finite global grounding while permitting incomplete searches to be acknowledged as such. The paper also introduces two calculations leveraging retained proof histories, focusing on uncertainty propagation in proof search, which is significant for AI and automated reasoning.
Key facts
- Paper arXiv:2608.09190 introduces structure-preserving uncertainty propagation in first-order proof search.
- GK is a query-directed first-order prover extending resolution-based proof search.
- GK includes explicit positive and negative claims, numerical confidence values, and prioritized default rules with exceptions.
- GK works directly with non-ground clauses, including equality and function terms.
- Candidate proofs are found by bounded first-order proof search.
- Exception conditions of defaults are checked by further bounded searches, recursively.
- The method avoids requiring a finite global grounding.
- The paper adds two calculations using retained proof histories: one computes probability of at least one retained proof without counting shared premises independently; the second resolves p (cut off).
Entities
Institutions
- arXiv