<p>According to <a href="https://arxiv.org/pdf/1011.0317.pdf" rel="nofollow noreferrer">Negative translations not intuitionistically
equivalent to the usual ones</a>,</p>
<blockquote>
<p>The image of the usual negative translations is (essentially) the negative fragment
NF, that is the set of all formulas without ∨ and ∃ and whose atomic formulas are
all negated</p>
</blockquote>
<p>If you look at the rules given at page 3 (or <a href="https://plato.stanford.edu/entries/logic-intuitionistic/#TraClaIntLog" rel="nofollow noreferrer">here</a>), it should be unsurprising that the translation is called negative. The fragment as defined by Harper removes the requirement that</p>
<blockquote>
<p>atomic formulas are
all negated</p>
</blockquote>
Intuitionistic Propositional Logic
<p>I have been looking into intuitionistic logic and what is called &quot;negative fragment&quot; of intuitionistic propositional logic. However, I was not able to find any resource that explains the reason why it is called &quot;negative fragment&quot;.</p>
<p>Any references/suggestions?</p>