<?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>S1405-55462023000100315</article-id>
<article-id pub-id-type="doi">10.13053/cys-27-1-4542</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Fitch-Style Modal Necessity as a Substructural Sequent-Style System]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Miranda-Perea]]></surname>
<given-names><![CDATA[Favio E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Estrada Zavaleta]]></surname>
<given-names><![CDATA[Ximena]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González Huesca]]></surname>
<given-names><![CDATA[Lourdes del Carmen]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2023</year>
</pub-date>
<volume>27</volume>
<numero>1</numero>
<fpage>315</fpage>
<lpage>326</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462023000100315&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462023000100315&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462023000100315&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The question of defining a Ja&#347;kowski-Fitch natural deduction system for modal logic has been settled since the very introduction of such formalisms in the middle of the last century. In contrast, a sequent-style formulation of this approach has only been discussed since the turn of this century but exclusively from the point of view of type theories. In this paper we propose a substructural sequent-style deductive system, based on previous ideas by Borghuis and Clouston, which captures Fitch-style for modal logic in a faithful way, meaning that the features of the original diagrammatic proofs are enforced by the sequent rules. This answers the question of what is a sequent-style version of Fitch-style natural deduction in the case of the necessity fragment of minimal modal logic    S 4.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Natural deduction]]></kwd>
<kwd lng="en"><![CDATA[fitch-style]]></kwd>
<kwd lng="en"><![CDATA[modal necessity]]></kwd>
<kwd lng="en"><![CDATA[substructural logics]]></kwd>
<kwd lng="en"><![CDATA[sequents]]></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[Borghuis]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Interpreting modal natural deduction in type theory]]></source>
<year>1993</year>
<page-range>67-102</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Borghuis]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modal pure type systems]]></article-title>
<source><![CDATA[Journal of Logic, Language and Information]]></source>
<year>1998</year>
<volume>7</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>265-96</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Borghuis]]></surname>
<given-names><![CDATA[V. A. J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Coming to terms with modal logic: on the interpretation of modalities in typed lambda-calculus]]></source>
<year>1994</year>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clouston]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Fitch-style modal lambda calculi]]></source>
<year>2018</year>
<page-range>258-75</page-range><publisher-name><![CDATA[Foundations of Software Science and Computation Structures]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fitch]]></surname>
<given-names><![CDATA[F. B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Symbolic logic: An introduction]]></source>
<year>1952</year>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fitting]]></surname>
<given-names><![CDATA[M. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proof methods for modal and intuitionistic logics]]></source>
<year>1983</year>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gentzen]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Untersuchungen über das logische schließen. I]]></article-title>
<source><![CDATA[Mathematische Zeitschrift]]></source>
<year>1935</year>
<volume>39</volume>
<page-range>176-210</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ja&#347;kowski]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[On the Rules of Suppositions in Formal Logic]]></source>
<year>1934</year>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kakutani]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Murase]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Nishiwaki]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dual-context modal logic as left adjoint of Fitch-style modal logic]]></article-title>
<source><![CDATA[Journal of Information Processing Systems]]></source>
<year>2019</year>
<volume>27</volume>
<page-range>77-86</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Siemens]]></surname>
<given-names><![CDATA[D. F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fitch-style rules for many modal logics]]></article-title>
<source><![CDATA[Notre Dame Journal of Formal Logic]]></source>
<year>1977</year>
<volume>18</volume>
<numero>4</numero>
<issue>4</issue>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Westrhenen]]></surname>
<given-names><![CDATA[S. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Sommerhalder]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Tonino]]></surname>
<given-names><![CDATA[J. F. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[ogica: een inleiding met toepassingen in de informatica]]></source>
<year>1993</year>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vaz de Paiva]]></surname>
<given-names><![CDATA[V. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Ritter]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Basic constructive modality]]></source>
<year>2011</year>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[von Plato]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elements of logical reasoning]]></source>
<year>2014</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
