Logic in Computer Science, Symposium on (2006)
Aug. 12, 2006 to Aug. 15, 2006
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2006.21
Ugo Dal Lago , Universite Paris 13, France
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity: it is both an upper bound to normalization time (modulo a polynomial overhead, independently on the reduction strategy) and a lower bound to the number of steps to normal form (for certain reduction strategies). Weights are then exploited in proving strong soundness theorems for various subsystems of linear logic, namely elementary linear logic, soft linear logic and light linear logic.
U. D. Lago, "Context Semantics, Linear Logic and Computational Complexity," 21st Annual IEEE Symposium on Logic in Computer Science(LICS), Seattle, WA, 2006, pp. 169-178.