<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04307724</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-25T08:51:58+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Projective relative unification through duality</title>
            <author role="crp">
              <persName>
                <forename type="first">Philippe</forename>
                <surname>Balbiani</surname>
              </persName>
              <email type="md5">941baf3268597ca0de5ccbd18874d4f4</email>
              <email type="domain">irit.fr</email>
              <idno type="idhal" notation="string">philippe-balbiani</idno>
              <idno type="idhal" notation="numeric">741408</idno>
              <idno type="halauthorid" notation="string">9601-741408</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3569-9160</idno>
              <idno type="IDREF">https://www.idref.fr/033316910</idno>
              <affiliation ref="#struct-400549"/>
              <affiliation ref="#struct-441569"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Quentin</forename>
                <surname>Gougeon</surname>
              </persName>
              <email type="md5">019fc22d9d638d5e6fd3314188f11e24</email>
              <email type="domain">irit.fr</email>
              <idno type="idhal" notation="numeric">1159256</idno>
              <idno type="halauthorid" notation="string">2573890-1159256</idno>
              <affiliation ref="#struct-34499"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Philippe</forename>
                <surname>Balbiani</surname>
              </persName>
              <email type="md5">941baf3268597ca0de5ccbd18874d4f4</email>
              <email type="domain">irit.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2023-11-26 15:00:02</date>
              <date type="whenModified">2025-10-22 18:04:09</date>
              <date type="whenReleased">2023-11-27 09:23:24</date>
              <date type="whenProduced">2023-10-02</date>
              <date type="whenEndEmbargoed">2024-04-03</date>
              <ref type="file" target="https://hal.science/hal-04307724v1/document">
                <date notBefore="2024-04-03"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04307724v1/file/main.pdf" id="file-4307724-3757237">
                <date notBefore="2024-04-03"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="590483">
                <persName>
                  <forename>Philippe</forename>
                  <surname>Balbiani</surname>
                </persName>
                <email type="md5">941baf3268597ca0de5ccbd18874d4f4</email>
                <email type="domain">irit.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04307724</idno>
            <idno type="halUri">https://hal.science/hal-04307724</idno>
            <idno type="halBibtex">balbiani:hal-04307724</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Logic and Computation&lt;/i&gt;, 2023, pp.1--21. &lt;a target="_blank" href="https://dx.doi.org/10.1093/logcom/exad058"&gt;&amp;#x27E8;10.1093/logcom/exad058&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Logic and Computation, 2023, pp.1--21. &amp;#x27E8;10.1093/logcom/exad058&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4307724-3757237"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="IRIT">IRIT - Institut de Recherche en Informatique de Toulouse</idno>
            <idno type="stamp" n="IRIT-LILAC" corresp="IRIT">Logique, Interaction, Langue et Calcul</idno>
            <idno type="stamp" n="IRIT-IA" corresp="IRIT">Intelligence Artificielle</idno>
            <idno type="stamp" n="TOULOUSE-INP">Toulouse - INP</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Projective relative unification through duality</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Philippe</forename>
                    <surname>Balbiani</surname>
                  </persName>
                  <email type="md5">941baf3268597ca0de5ccbd18874d4f4</email>
                  <email type="domain">irit.fr</email>
                  <idno type="idhal" notation="string">philippe-balbiani</idno>
                  <idno type="idhal" notation="numeric">741408</idno>
                  <idno type="halauthorid" notation="string">9601-741408</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3569-9160</idno>
                  <idno type="IDREF">https://www.idref.fr/033316910</idno>
                  <affiliation ref="#struct-400549"/>
                  <affiliation ref="#struct-441569"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Quentin</forename>
                    <surname>Gougeon</surname>
                  </persName>
                  <email type="md5">019fc22d9d638d5e6fd3314188f11e24</email>
                  <email type="domain">irit.fr</email>
                  <idno type="idhal" notation="numeric">1159256</idno>
                  <idno type="halauthorid" notation="string">2573890-1159256</idno>
                  <affiliation ref="#struct-34499"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">6267</idno>
                <idno type="issn">0955-792X</idno>
                <idno type="eissn">1465-363X</idno>
                <title level="j">Journal of Logic and Computation</title>
                <imprint>
                  <publisher>Oxford University Press (OUP)</publisher>
                  <biblScope unit="pp">1--21</biblScope>
                  <date type="datePub">2023-10-02</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1093/logcom/exad058</idno>
              <ref type="publisher">https://academic.oup.com/logcom/advance-article-abstract/doi/10.1093/logcom/exad058/7286973?redirectedFrom=fulltext</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="info">Computer Science [cs]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Unification problems can be formulated and investigated in an algebraic setting, by identifying substitutions to modal algebra homomorphisms. This opens the door to applications of the notorious duality between Heyting or modal algebras and descriptive frames. Through substantial use of this correspondence, we give a necessary and sufficient condition for formulas to be projective. A close inspection of this characterization will motivate a generalization of standard unification, which we dub relative unification. Applying this result to a number of different logics, we then obtain new proofs of their projective-or non-projective-character. Aside from reproving known results, we show that the projective extensions of K5 are exactly the extensions of K45. This resolves the open question of whether K5 is projective.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-400549" status="OLD">
          <orgName>Logique, Interaction, Langue et Calcul</orgName>
          <orgName type="acronym">IRIT-LILaC</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>IRIT118 Route de Narbonne31062 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.irit.fr/departement/intelligence-artificielle/equipe-lilac/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-34499" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-217752" type="indirect"/>
            <relation name="UMR5505 / URA1399" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
            <relation active="#struct-1149079" type="indirect"/>
            <relation name="FED4171" active="#struct-217752" type="indirect"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-34499" status="OLD">
          <idno type="IdRef">030947448</idno>
          <idno type="ISNI">0000000121927225</idno>
          <idno type="RNSR">199511949P</idno>
          <idno type="ROR">https://ror.org/01rx4qw44</idno>
          <orgName>Institut de recherche en informatique de Toulouse</orgName>
          <orgName type="acronym">IRIT</orgName>
          <date type="start">1990-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 Route de Narbonne, F-31062 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.irit.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UMR5505 / URA1399" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
            <relation active="#struct-1149079" type="direct"/>
            <relation name="FED4171" active="#struct-217752" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-448187" status="VALID">
          <idno type="IdRef">026388820</idno>
          <idno type="ISNI">0000000121766169</idno>
          <idno type="ROR">https://ror.org/033p9g875</idno>
          <orgName>Institut National Polytechnique (Toulouse)</orgName>
          <orgName type="acronym">Toulouse INP</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.inp-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-1149079" status="OLD">
          <orgName>Toulouse Mind &amp; Brain Institut</orgName>
          <orgName type="acronym">TMBI</orgName>
          <date type="start">2021-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>CHU Purpan, Pavillon Baudot, 31059 Toulouse cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.tmbi.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation name="FED4171" active="#struct-217752" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>