Abstract
We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But we also find that the guarded version of a least fixed point algorithm may have a greater time complexity than the unguarded version, by a linear factor.
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