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......@@ -9964,3 +9964,21 @@ abstract =
We verify the correctness of Prim's, Kruskal's and
Borůvka's minimum spanning tree algorithms based on algebras for
aggregation and minimisation.
[Topological_Semantics]
title = Topological semantics for paraconsistent and paracomplete logics
author = David Fuenmayor <mailto:davfuenmayor@gmail.com>
topic = Logic/General logic
date = 2020-12-17
notify = davfuenmayor@gmail.com
abstract =
We introduce a generalized topological semantics for paraconsistent
and paracomplete logics by drawing upon early works on topological
Boolean algebras (cf. works by Kuratowski, Zarycki, McKinsey &
Tarski, etc.). In particular, this work exemplarily illustrates the
shallow semantical embeddings approach (<a
href="http://dx.doi.org/10.1007/s11787-012-0052-y">SSE</a>)
employing the proof assistant Isabelle/HOL. By means of the SSE
technique we can effectively harness theorem provers, model finders
and 'hammers' for reasoning with quantified non-classical
logics.
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<h1> <font class="first">T</font>opological
semantics
for
paraconsistent
and
paracomplete
logics
</h1>
<p>&nbsp;</p>
<table width="80%" class="data">
<tbody>
<tr>
<td class="datahead" width="20%">Title:</td>
<td class="data" width="80%">Topological semantics for paraconsistent and paracomplete logics</td>
</tr>
<tr>
<td class="datahead">
Author:
</td>
<td class="data">
David Fuenmayor (davfuenmayor /at/ gmail /dot/ com)
</td>
</tr>
<tr>
<td class="datahead">Submission date:</td>
<td class="data">2020-12-17</td>
</tr>
<tr>
<td class="datahead" valign="top">Abstract:</td>
<td class="abstract mathjax_process">
We introduce a generalized topological semantics for paraconsistent
and paracomplete logics by drawing upon early works on topological
Boolean algebras (cf. works by Kuratowski, Zarycki, McKinsey &
Tarski, etc.). In particular, this work exemplarily illustrates the
shallow semantical embeddings approach (<a
href="http://dx.doi.org/10.1007/s11787-012-0052-y">SSE</a>)
employing the proof assistant Isabelle/HOL. By means of the SSE
technique we can effectively harness theorem provers, model finders
and 'hammers' for reasoning with quantified non-classical
logics.</td>
</tr>
<tr>
<td class="datahead" valign="top">BibTeX:</td>
<td class="formatted">
<pre>@article{Topological_Semantics-AFP,
author = {David Fuenmayor},
title = {Topological semantics for paraconsistent and paracomplete logics},
journal = {Archive of Formal Proofs},
month = dec,
year = 2020,
note = {\url{https://isa-afp.org/entries/Topological_Semantics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="../browser_info/current/AFP/Topological_Semantics/outline.pdf">Proof outline</a><br>
<a href="../browser_info/current/AFP/Topological_Semantics/document.pdf">Proof document</a>
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......@@ -88,6 +88,14 @@ of a scientific journal, is indexed by <a href="http://dblp.uni-trier.de/db/jour
<tr>
<td class="head">2020</td>
</tr>
<tr>
<td class="entry">
2020-12-17: <a href="entries/Topological_Semantics.html">Topological semantics for paraconsistent and paracomplete logics</a>
<br>
Author:
David Fuenmayor
</td>
</tr>
<tr>
<td class="entry">
2020-12-08: <a href="entries/Relational_Minimum_Spanning_Trees.html">Relational Minimum Spanning Tree Algorithms</a>
......
......@@ -9,7 +9,25 @@
and larger scientific developments, mechanically checked
in the theorem prover Isabelle.
</description>
<pubDate>08 Dec 2020 00:00:00 +0000</pubDate>
<pubDate>17 Dec 2020 00:00:00 +0000</pubDate>
<item>
<title>Topological semantics for paraconsistent and paracomplete logics</title>
<link>https://www.isa-afp.org/entries/Topological_Semantics.html</link>
<guid>https://www.isa-afp.org/entries/Topological_Semantics.html</guid>
<dc:creator> David Fuenmayor </dc:creator>
<pubDate>17 Dec 2020 00:00:00 +0000</pubDate>
<description>
We introduce a generalized topological semantics for paraconsistent
and paracomplete logics by drawing upon early works on topological
Boolean algebras (cf. works by Kuratowski, Zarycki, McKinsey &amp;
Tarski, etc.). In particular, this work exemplarily illustrates the
shallow semantical embeddings approach (&lt;a
href=&#34;http://dx.doi.org/10.1007/s11787-012-0052-y&#34;&gt;SSE&lt;/a&gt;)
employing the proof assistant Isabelle/HOL. By means of the SSE
technique we can effectively harness theorem provers, model finders
and &#39;hammers&#39; for reasoning with quantified non-classical
logics.</description>
</item>
<item>
<title>Relational Minimum Spanning Tree Algorithms</title>
<link>https://www.isa-afp.org/entries/Relational_Minimum_Spanning_Trees.html</link>
......@@ -574,20 +592,5 @@ several properties such as strong normalization, the subterm property,
closure properties under substitutions and contexts, as well as ground
totality.</description>
</item>
<item>
<title>Irrationality Criteria for Series by Erdős and Straus</title>
<link>https://www.isa-afp.org/entries/Irrational_Series_Erdos_Straus.html</link>
<guid>https://www.isa-afp.org/entries/Irrational_Series_Erdos_Straus.html</guid>
<dc:creator> Angeliki Koutsoukou-Argyraki, Wenda Li </dc:creator>
<pubDate>12 May 2020 00:00:00 +0000</pubDate>
<description>
We formalise certain irrationality criteria for infinite series of the form:
\[\sum_{n=1}^\infty \frac{b_n}{\prod_{i=1}^n a_i} \]
where $\{b_n\}$ is a sequence of integers and $\{a_n\}$ a sequence of positive integers
with $a_n &gt;1$ for all large n. The results are due to P. Erdős and E. G. Straus
&lt;a href=&#34;https://projecteuclid.org/euclid.pjm/1102911140&#34;&gt;[1]&lt;/a&gt;.
In particular, we formalise Theorem 2.1, Corollary 2.10 and Theorem 3.1.
The latter is an application of Theorem 2.1 involving the prime numbers.</description>
</item>
</channel>
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......@@ -515,6 +515,7 @@
</div>
<h3>General logic</h3>
<div class="list">
<a href="entries/Topological_Semantics.html">Topological_Semantics</a> &nbsp;
<strong>Classical propositional logic:</strong>
<a href="entries/Free-Boolean-Algebra.html">Free-Boolean-Algebra</a> &nbsp;
<strong>Classical first-order logic:</strong>
......
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