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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Famous quotes containing the word logic:
“We want in every man a long logic; we cannot pardon the absence of it, but it must not be spoken. Logic is the procession or proportionate unfolding of the intuition; but its virtue is as silent method; the moment it would appear as propositions and have a separate value, it is worthless.”
—Ralph Waldo Emerson (1803–1882)