Bounded functional interpretation

@article{citeulike:131997, abstract = {We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Godel's functional "Dialectica" interpretation, the new interpretation 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.}, author = {Ferreira, Fernando and Oliva, Paulo }, citeulike-article-id = {131997}, doi = {http://dx.doi.org/10.1016/j.apal.2004.11.001}, journal = {Annals of Pure and Applied Logic}, keywords = {bounded\_arithmetic}, posted-at = {2005-03-18 11:15:41}, priority = {2}, title = {Bounded functional interpretation}, url = {http://dx.doi.org/10.1016/j.apal.2004.11.001}, volume = {In Press, Corrected Proof} }

TY - JOUR ID - citeulike:131997 L3 - citeulike-article-id:131997 N2 - We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Godel's functional "Dialectica" interpretation, the new interpretation 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. JF - Annals of Pure and Applied Logic TI - Bounded functional interpretation VL - In Press, Corrected Proof KW - bounded_arithmetic AU - Ferreira, Fernando AU - Oliva, Paulo UR - http://dx.doi.org/10.1016/j.apal.2004.11.001 ER -