@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              We show that it is equivalent, for certain sets of finite graphs, to be definable in CMS (counting monadic second-order logic, a natural extension of monadic second-order logic), and to be recognizable in an algebraic framework induced by the notion of modular decomposition of a finite graph. More precisely, we consider the set $F_\\infty$ of composition operations on graphs which occur in the modular decomposition of finite graphs. If $F$ is a subset of $F_{\\infty}$, we say that a graph is an $\\calF$-graph if it can be decomposed using only operations in $F$. A set of $F$-graphs is recognizable if it is a union of classes in a finite-index equivalence relation which is preserved by the operations in $F$. We show that if $F$ is finite and its elements enjoy only a limited amount of commutativity --- a property which we call weak rigidity, then recognizability is equivalent to CMS-definability. This requirement is weak enough to be satisfied whenever all $F$-graphs are posets, that is, transitive dags. In particular, our result generalizes Kuske's recent result on series-parallel poset languages.
            """ ;
    dct:identifier "hal-00092417" ;
    dct:issued "2026-05-07T15:36:27.503249"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-07T15:36:27.503253"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "On the logical definability of certain graph and poset languages" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
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    dcat:keyword "algebraic-recognizability",
        "graph-languages",
        "infoeu-reposemanticsarticle",
        "infoinfo-locomputer-science-cslogic-in-computer-science-cslo",
        "journal-articles",
        "logical-definability",
        "msc-03b70-68q60-68q70" ;
    dcat:landingPage <Journal%20of%20Automata%2C%20Languages%20and%20Computation> .

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    dct:issued "2026-05-07T15:36:27.509864"^^xsd:dateTime ;
    dct:modified "2026-05-07T15:36:27.495079"^^xsd:dateTime ;
    dct:title "On the logical definability of certain graph and poset languages" ;
    dcat:accessURL <https://hal.science/hal-00092417> .

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