Functional interpretations are interpretations of non-constructive theories in functional ones.
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This truth-functional interpretation of implication is called material implication or material conditional.
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Functional interpretations usually proceed in two stages.
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Functional interpretations also provide a way to extract constructive information from proofs in the reduced theory.
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Functional interpretations of hypostome shape also allow for reasonable speculation on the feeding habits of trilobite species.
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Successful functional interpretations have yielded reductions of infinitary theories to finitary theories and impredicative theories to predicative ones.
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Functional interpretations have also been used to provide ordinal analyses of theories and classify their provably recursive functions.
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The study of functional interpretations began with Kurt G�del's interpretation of intuitionistic arithmetic in a quantifier-free theory of functionals finite type.
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Another database, Termini oriented protein Function Inferred Database ( TopFIND ), serves as a knowledge base to integrate protein termini formed by protease processing with functional interpretations.
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Maps can depict functional interpretations of specific properties such as critical heavy-metal levels or can depict interpretation of multiple properties such as a map of erosion risk index.
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