Modal Logic For Computability
Kleene's original realizability interpretation has received much attention among those who study connections between computability and logic. It was extended to full higher-order intuitionistic logic by Martin Hyland in 1982 who constructed the effective topos. In 2002, Steven Awodey, Lars Birkedal, and Dana Scott formulated a modal logic for computability which extended the usual realizability interpretation with two modal operators expressing the notion of being "computably true".
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