Negative translations not intuitionistically equivalent to the usual ones
Jaime Gaspar
TL;DR
This paper demonstrates that not all negative translations are intuitionistically equivalent by providing counterexamples and characterizes those that are equivalent to the usual negative translation.
Contribution
It refutes the conjecture that all negative translations are intuitionistically equivalent and characterizes the ones that are.
Findings
Counterexamples show some negative translations are not intuitionistically equivalent.
Characterization of negative translations equivalent to the usual one.
Refutation of a previously held conjecture.
Abstract
We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.
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Taxonomy
TopicsLogic, programming, and type systems · Logic, Reasoning, and Knowledge · Computability, Logic, AI Algorithms