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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Higher order quantum map types are identified with Boolean type functions, with comb types corresponding to chain posets, and type functions decomposed via max/min of basic chains corresponding to affine mixtures and intersections.
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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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On the structure of higher order quantum maps
Higher order quantum map types are identified with Boolean type functions, with comb types corresponding to chain posets, and type functions decomposed via max/min of basic chains corresponding to affine mixtures and intersections.