Deductive closure

<h2 id="examples">Examples</h2>
<p>In <a href="/facts/Propositional_calculus/MNt5v31V">propositional logic</a>, the set of all true propositions is deductively closed. This is to say that only true statements are derivable from other true statements.
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<h2 id="epistemic-closure">Epistemic closure</h2>
<p class="note">Main article: <a href="/facts/Epistemic_closure/TLNJ5n57">Epistemic closure</a></p>
<p>In <a href="/facts/Epistemology/NsDwpcYH">epistemology</a>, many philosophers have and continue to debate whether particular subsets of <a href="/facts/Proposition/0877MFMD">propositions</a>—especially ones ascribing <a href="/facts/Knowledge/joozoaup">knowledge</a> or <a href="/facts/Theory_of_justification/CxWaj0pY">justification</a> of a <a href="/facts/Belief/HbPvkGT6">belief</a> to a subject—are closed under deduction.
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<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>First-order theory at PlanetMath. <a href="https://planetmath.org/firstordertheory" target="_blank">https://planetmath.org/firstordertheory</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
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Deductive closure open-in-new

Deductive closure