pQLL calculi assign real-valued strength to proofs, generalize hypersequent and deep inference systems, prove cut elimination, and achieve completeness for soft residuated lattices, recovering MALL as p goes to infinity.
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QLL is a novel logic for neuro-symbolic learning that uses ML-native operations (sum, log-sum-exp) on logits to embed constraints, satisfying most linear logic properties and showing stronger correlation between empirical robustness and formal verification than prior approaches.
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Quantitative Linear Logic
pQLL calculi assign real-valued strength to proofs, generalize hypersequent and deep inference systems, prove cut elimination, and achieve completeness for soft residuated lattices, recovering MALL as p goes to infinity.
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Quantitative Linear Logic for Neuro-Symbolic Learning and Verification
QLL is a novel logic for neuro-symbolic learning that uses ML-native operations (sum, log-sum-exp) on logits to embed constraints, satisfying most linear logic properties and showing stronger correlation between empirical robustness and formal verification than prior approaches.