<?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>1405-5546</journal-id>
<journal-title><![CDATA[Computación y Sistemas]]></journal-title>
<abbrev-journal-title><![CDATA[Comp. y Sist.]]></abbrev-journal-title>
<issn>1405-5546</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico Nacional, Centro de Investigación en Computación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-55462022000200801</article-id>
<article-id pub-id-type="doi">10.13053/cys-26-2-4246</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An Algebraic Study of the First Order Version of some Implicational Fragments of Three-Valued &#321;ukasiewicz Logic]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Figallo-Orellano]]></surname>
<given-names><![CDATA[Aldo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Slagter]]></surname>
<given-names><![CDATA[Juan Sebastián]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional del Sur Departamento de Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,University of Campinas Centre for Logic, Epistemology and The History of Science ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brazil</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>26</volume>
<numero>2</numero>
<fpage>801</fpage>
<lpage>813</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462022000200801&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462022000200801&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462022000200801&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In this paper, some implicational fragments of trivalent &#321;ukasiewicz logic are studied and the propositional and first-order logic are presented. The maximal consistent theories are studied as Monteiro&#8217;s maximal deductive systems of the Lindenbaum-Tarski algebra in both cases. Consequently, the adequacy theorems with respect to the suitable algebraic structures are proven.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Trivalent Hilbert algebras]]></kwd>
<kwd lng="en"><![CDATA[modals operators]]></kwd>
<kwd lng="en"><![CDATA[3-valued Gödel logic]]></kwd>
<kwd lng="en"><![CDATA[first-order logics]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bell]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Slomson]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Models and Ultraproducts: An Introduction]]></source>
<year>1971</year>
<publisher-loc><![CDATA[North Holland, Amsterdam ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Boicescu]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Filipoiu]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Georgescu]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Rudeanu]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lukasiewicz - Moisil Algebras]]></article-title>
<source><![CDATA[Annals of Discrete Mathematics]]></source>
<year>1991</year>
<volume>49</volume>
<publisher-loc><![CDATA[North - Holland ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cignoli]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An algebraic approach to elementary theories based on n-valued &#321;ukasiewicz logics]]></article-title>
<source><![CDATA[Z. Math. Logik Grundlag. Math.]]></source>
<year>1984</year>
<volume>30</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>87-96</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cignoli]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proper n-valued &#321;ukasiewicz algebras as S-algebras of &#321;ukasiewicz n-valued propositional calculi]]></article-title>
<source><![CDATA[Studia Logica]]></source>
<year>1982</year>
<volume>41</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>3-16</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ciucci]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Dubois]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Three-valued logics for incomplete information and epistemic logic]]></source>
<year>2012</year>
<conf-name><![CDATA[ European Workshop on Logics in Artificial Intelligence]]></conf-name>
<conf-loc> </conf-loc>
<page-range>147-59</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Canals Frau]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Figallo]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Modal three-valued Hilbert algebras]]></source>
<year>1990</year>
<page-range>1-21</page-range><publisher-name><![CDATA[Instituto de Ciencias Básicas, Universidad Nacional de San Juan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Canals Frau]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Figallo]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Modal 3-valued implicative semilattices]]></source>
<year>1992</year>
<page-range>1-24</page-range><publisher-name><![CDATA[Instituto de Ciencias Básicas, Universidad Nacional de San Juan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Diego]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sur les algčbres de Hilbert]]></article-title>
<source><![CDATA[Colléction de Logique Mathčmatique]]></source>
<year>1966</year>
<numero>21</numero>
<issue>21</issue>
<publisher-name><![CDATA[Gouthier-Villars]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Figallo]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramón]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A note on the Hilbert algebras with infimum]]></article-title>
<source><![CDATA[Mat. Contemp.]]></source>
<year>2003</year>
<volume>24</volume>
<page-range>23-37</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Figallo]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramón]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Saad]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[iH-Propositional calculus]]></article-title>
<source><![CDATA[Bull. Sect. Logic Univ. Lodz]]></source>
<year>2006</year>
<volume>35</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>157-62</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Figallo Jr.]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Ziliani]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Remarks on Hertz algebras and implicative semilattices]]></article-title>
<source><![CDATA[Bull. Sect. Logic Univ. Lódz]]></source>
<year>2005</year>
<volume>34</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>37-42</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hernández-Tello]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Arrazola-Ramírez]]></surname>
<given-names><![CDATA[J.R.]]></given-names>
</name>
<name>
<surname><![CDATA[Osorio-Galindo]]></surname>
<given-names><![CDATA[M.J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The pursuit of an implication for the logics L3A and L3B]]></article-title>
<source><![CDATA[Logica Universalis]]></source>
<year>2017</year>
<volume>11</volume>
<page-range>507-24</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monteiro]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sur les algčbres de Heyting simetriques]]></article-title>
<source><![CDATA[Portugaliae Math.]]></source>
<year>1980</year>
<volume>39</volume>
<numero>1-4</numero>
<issue>1-4</issue>
<page-range>1-237</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monteiro]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Les algčbras de Hilbert linaires, Unpublished papers I]]></article-title>
<source><![CDATA[Notas de Lógica Matemtica]]></source>
<year>1996</year>
<volume>40</volume>
<page-range>114-27</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monteiro]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Algčbres de Hilbert n&#8722;valentes]]></article-title>
<source><![CDATA[Portugaliae Math.]]></source>
<year>1977</year>
<volume>36</volume>
<page-range>159-74</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monteiro]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Algebras de &#321;ukasiewicz trivalentes monádicas]]></source>
<year>1973</year>
<publisher-name><![CDATA[Universidad Nacional del Sur]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pérez-Gaspar]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Hernández-Tello]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Arrazola-Ramírez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Osorio-Galindo]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An axiomatic approach to CG&#8217;3 logic]]></article-title>
<source><![CDATA[Logic Journal of the IGPL]]></source>
<year>2020</year>
<volume>28</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1218-32</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Osorio]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[arballido]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Zepeda]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[SP3B as an extension of C1]]></article-title>
<source><![CDATA[South American Journal of Logic]]></source>
<year>2018</year>
<volume>4</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-27</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Osorio]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Carballido]]></surname>
<given-names><![CDATA[J.L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Brief study of G&#8217;3 logic]]></article-title>
<source><![CDATA[Journal of Applied Non-Classical Logic]]></source>
<year>2008</year>
<volume>18</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>475-99</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Osorio]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Zepeda]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Nieves]]></surname>
<given-names><![CDATA[J.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Carballido]]></surname>
<given-names><![CDATA[J.L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[G&#8217;3&#8211;stable semantics and inconsistency]]></article-title>
<source><![CDATA[Computación y Sistemas]]></source>
<year>2009</year>
<volume>13</volume>
<page-range>75-86</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Osorio]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Navarro]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Arrazola]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Borja]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Logics with common weak completions]]></article-title>
<source><![CDATA[Journal of Logic and Computation]]></source>
<year>2006</year>
<volume>16</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>867-90</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[V.B.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-Gaspar]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Kripke-type semantics for CG&#8217;3]]></article-title>
<source><![CDATA[Electronic Notes in Theoretical Computer Science]]></source>
<year>2016</year>
<volume>328</volume>
<page-range>17-29</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mendelson]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to Mathematical Logic]]></source>
<year>2009</year>
<publisher-name><![CDATA[CRC Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Slagter]]></surname>
<given-names><![CDATA[J.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Reductos hilbertianos de las álgebras de &#321;ukasiewicz-Moisil de orden 3]]></source>
<year>2016</year>
<publisher-name><![CDATA[Universidad Nacional del Sur]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rasiowa]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An algebraic approach to non-clasical logics]]></article-title>
<source><![CDATA[Studies in logic and the foundations of mathematics]]></source>
<year>1974</year>
<volume>78</volume>
<publisher-loc><![CDATA[Amsterdam ]]></publisher-loc>
<publisher-name><![CDATA[North-Holland Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thomas]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Finite limitations on Dummett&#8217;s LC]]></article-title>
<source><![CDATA[Notre Dame Journal of Formal Logic]]></source>
<year>1962</year>
<volume>3</volume>
<page-range>170-4</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wójcicki]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Lectures on propositional calculi]]></source>
<year>1984</year>
<publisher-loc><![CDATA[Warsaw ]]></publisher-loc>
<publisher-name><![CDATA[Ossolineum]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
