Linear Logic For Generalized Quantum Mechanics
Vaughan Pratt · 2005
Quantum logic is static, describing automata having uncertain states but no state transitions and no Heisenberg uncertainty tradeoff. We cast Girard's linear logic in the role of a dynamic quantum logic, regarded as an extension of quantum logic with time nonstandardly interpreted over a domain of linear automata and their dual linear schedules. In this extension the uncertainty tradeoff emerges via the "structure veil." When VLSI shrinks to where quantum effects are felt, their computer-aided design systems may benefit from such logics of computational behavior having a strong connection to quantum mechanics. 1 Motivation VLSI designers will eventually need to reckon with quantum mechanics (QM), certainly within 50 years and possibly by the 2010's. Computer-aided design (CAD) tools will need to adapt accordingly. Does this entail changing only the theory or also the logic of CAD verification systems? That is, will it be enough just to change those nonlogical axioms defining how elect...