Context Semantics, Linear Logic and Computational Complexity

Details Context Semantics, Linear Logic and Computational Complexity Context Semantics, Linear Logic and Computational Complexity

2005-10-31

arxiv.org/abs/cs/0510092v3

Computer Science

Logic in Computer Science

22 pages

Scientific paper

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.

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