Automated quantum reasoning: non-logic -> semi-logic -> hyper-logic

Bob Coecke

Quantum theory does not necessitate the breakdown of full-blown deduction. On the contrary, it comes with substantially enhanced logical reasoning power as compared to its classical counterpart. It features a co-deductive mechanism besides a deductive one, resulting in a sound purely graphical calculus which admits an information-flow interpretation. The key physical concept represented by the logic is the interaction of quantum systems i.e.~the tensor product structure, contra Birkhoff-von Neumann-logic (BvN-logic) which only addresses individual systems. The trace structure, important in IR applications, is an intrincic part of the logic, together with many other quantitative concepts, again contra BvN-logic where the trace only arises indirectly via Gleason's theorem. Hence we provide a powerful high-level formalism for designing, controlling and even automating quantum informatic tasks, which can involve multiple agents. We also mention several existing applications to non-quantum domains such as linguistics, multi-agent systems and concurrency.

Subjects: 9.3 Mathematical Foundations; 3. Automated Reasoning

Submitted: Jan 23, 2007

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