<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0370-3908</journal-id>
<journal-title><![CDATA[Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. acad. colomb. cienc. exact. fis. nat.]]></abbrev-journal-title>
<issn>0370-3908</issn>
<publisher>
<publisher-name><![CDATA[Academia Colombiana de Ciencias Exactas, Físicas y Naturales]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0370-39082022000200311</article-id>
<article-id pub-id-type="doi">10.18257/raccefyn.1625</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Lógica cuántica: enfoque reticular ortocomplementado modular y tesis de la interpretación parcial]]></article-title>
<article-title xml:lang="en"><![CDATA[Quantum logic: modular orthocomplemented lattice approach and partial interpretation thesis]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Villacís]]></surname>
<given-names><![CDATA[Carlos]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Complutense de Madrid Facultad de Filosofía ]]></institution>
<addr-line><![CDATA[Madrid ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>46</volume>
<numero>179</numero>
<fpage>311</fpage>
<lpage>324</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0370-39082022000200311&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0370-39082022000200311&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0370-39082022000200311&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En el presente artículo se propone una concepción de la lógica cuántica como forma de interpretación de la mecánica cuántica. Se establece como hipótesis metodológica la tesis metateórica de la interpretación parcial para realizar una reconstrucción del enfoque reticular ortocomplementado modular con el cual Birkhoff y von Neumann iniciaron el desarrollo de la lógica cuántica. Sobre estas bases se elabora una modelización lógica del cálculo proposicional obtenido en comparación analítica con otras estructuras lógico-algebraicas. Se discuten los resultados a partir de la propiedad distributiva y de la capacidad para retener la propiedad de la modularidad. Por último, se ponen de manifiesto problemas heurísticos y formales con respecto al éxito de la consecución de tal núcleo conceptual.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this article, a conception of quantum logic is proposed as a way of interpreting quantum mechanics. The metatheoretical thesis of partial interpretation is established as a methodological hypothesis to carry out a reconstruction of the modular orthocomplemented lattice approach with which Birkhoff and von Neumann began the development of quantum logic. On these bases, the logical modeling of the propositional calculus obtained is elaborated via an analytical comparison with other logical-algebraic structures. The results are discussed from the distributive property and the ability to retain the property of modularity. Finally, heuristic and formal problems are revealed regarding the success of achieving such a conceptual core.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Mecánica cuántica]]></kwd>
<kwd lng="es"><![CDATA[Lógica cuántica]]></kwd>
<kwd lng="es"><![CDATA[Interpretación parcial]]></kwd>
<kwd lng="es"><![CDATA[Modularidad]]></kwd>
<kwd lng="es"><![CDATA[Retículo]]></kwd>
<kwd lng="en"><![CDATA[Quantum mechanics]]></kwd>
<kwd lng="en"><![CDATA[Quantum logic]]></kwd>
<kwd lng="en"><![CDATA[Partial interpretation]]></kwd>
<kwd lng="en"><![CDATA[Modularity]]></kwd>
<kwd lng="en"><![CDATA[Lattice]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aerts]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Quantum Axiomatics]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Engesser]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Gabbay]]></surname>
<given-names><![CDATA[D.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Lehmann]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of Quantum Logic and Quantum Structures]]></source>
<year>2009</year>
<page-range>79-126</page-range><publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
<publisher-name><![CDATA[North-Holland]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Birkhoff]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Combinatorial Relations in Projective Geometries]]></article-title>
<source><![CDATA[Annals of Mathematics]]></source>
<year>1935</year>
<volume>36</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>743-8</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Birkhoff]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<source><![CDATA[Lattice Theory]]></source>
<year>1948</year>
<page-range>1-283</page-range><publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[American Mathematical Society]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Birkhoff]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[von Neumann]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Logic of Quantum Mechanics]]></article-title>
<source><![CDATA[Annals of Mathematics]]></source>
<year>1936</year>
<volume>37</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>823-42</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dalla Chiara]]></surname>
<given-names><![CDATA[M.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Giuntini]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Quantum Logics]]></source>
<year>2008</year>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dalla Chiara]]></surname>
<given-names><![CDATA[M.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Giuntini]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Rédei]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The History of Quantum Logic]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Gabbay]]></surname>
<given-names><![CDATA[D.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Woods]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of the History of Logic: Volume 8: the Many Valued and Nonmonotonic Turn in Logic]]></source>
<year>2007</year>
<page-range>205-83</page-range><publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
<publisher-name><![CDATA[North-Holland]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Février]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<source><![CDATA[Les relations d'incertitude de Heisenberg et la logique]]></source>
<year>1937</year>
<numero>6</numero>
<conf-name><![CDATA[ Travaux du IXe Congrès International de Philosophie]]></conf-name>
<conf-loc> </conf-loc>
<issue>6</issue>
<page-range>88-94</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grätzer]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<source><![CDATA[Lattice Theory Foundation]]></source>
<year>2011</year>
<page-range>1-613</page-range><publisher-loc><![CDATA[Birkhauser. Basilea ]]></publisher-loc>
<publisher-name><![CDATA[Birkhauser]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jammer]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in historical perspective]]></source>
<year>1974</year>
<page-range>1-536</page-range><publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jauch]]></surname>
<given-names><![CDATA[J.M]]></given-names>
</name>
</person-group>
<source><![CDATA[Foundations of Quantum Mechanics]]></source>
<year>1968</year>
<page-range>1-299</page-range><publisher-loc><![CDATA[Massachusetts ]]></publisher-loc>
<publisher-name><![CDATA[Addison-Wesley Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jordan]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<source><![CDATA[Ueber eine Klasse nichtassoziativer hyperkomplexer Algebren]]></source>
<year>1932</year>
<page-range>569-75</page-range><publisher-name><![CDATA[Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mackey]]></surname>
<given-names><![CDATA[G.W]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Foundations of Quantum Mechanics]]></source>
<year>1963</year>
<page-range>1-148</page-range><publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Benjamin]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piron]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Axiomatique Quantique]]></article-title>
<source><![CDATA[Helvetica Physica Acta]]></source>
<year>1964</year>
<volume>37</volume>
<page-range>439-68</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Popper]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Birkhoff and von Neumann's Interpretation of Quantum Mechanics]]></article-title>
<source><![CDATA[Nature]]></source>
<year>1968</year>
<volume>219</volume>
<page-range>682-5</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rédei]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Birkhoff-von Neumann Concept of Quantum Logic]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Engesser]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Gabbay]]></surname>
<given-names><![CDATA[D.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Lehmann]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of Quantum Logic and Quantum Structures]]></source>
<year>2009</year>
<page-range>1-22</page-range><publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
<publisher-name><![CDATA[North-Holland]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reichenbach]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<source><![CDATA[Philosophic Foundations of Quantum Mechanics]]></source>
<year>1944</year>
<page-range>1-189</page-range><publisher-loc><![CDATA[California ]]></publisher-loc>
<publisher-name><![CDATA[University of California Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Segal]]></surname>
<given-names><![CDATA[I.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Postulates for General Quantum Mechanics]]></article-title>
<source><![CDATA[Annals of Mathematics]]></source>
<year>1947</year>
<volume>48</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>930-48</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[van Fraassen]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Labyrinth of Quantum Logics]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Cohen]]></surname>
<given-names><![CDATA[R.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Wartofsky]]></surname>
<given-names><![CDATA[M.W]]></given-names>
</name>
</person-group>
<source><![CDATA[Boston Studies in the Philosophy of Science Vol. XIII. Logical and Epistemological Studies in Contemporary Physics.]]></source>
<year>1974</year>
<page-range>224-54</page-range><publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Reidel Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[von Neumann]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematische Grundlagen der Quantenmechanik]]></source>
<year>1932</year>
<page-range>1-262</page-range><publisher-loc><![CDATA[Berlín ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
