Bounded functional interpretation

We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Godel's functional "Dialectica" interpretation, the new interpre- tation does not care for precise witnesses of existential statements, but only for bounds for them. New principles are supported by our interpretation, including (a version of) the FAN theorem, weak Konig's lemma and the lesser limited principle of omniscience. Conspicuous among these principles are also refutations of some laws of classical logic. Notwithstanding, we end up discussing some applications of the new interpretation to theories of classical arithmetic and analysis.

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