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            <title xml:lang="en">Ordered sequents and proof nets</title>
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            <idno type="halRefHtml">Mathématiques [math]. Université Paris-Diderot - Paris VII, 1993. Français. &lt;a target="_blank" href="https://www.theses.fr/"&gt;&amp;#x27E8;NNT : &amp;#x27E9;&lt;/a&gt;</idno>
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                <authority type="supervisor">Jean-Yves Girard</authority>
                <authority type="jury">Jean-Yves Girard</authority>
                <authority type="jury">Jean-Louis Krivine</authority>
                <authority type="jury">Jean-Jacques Loeb</authority>
                <authority type="jury">Jacques van de Wiele</authority>
                <authority type="jury">Jacqueline Vauzeilles</authority>
                <authority type="jury">Gilles Zémor</authority>
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                <term xml:lang="en">linear logic</term>
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                <term xml:lang="en">partial orders</term>
                <term xml:lang="fr">logique linéaire</term>
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              <p>This thesis provides a sequent calculus for linear logic enriched with a non comutative and selfdual connective called "before", in between "par" and "times". It is defined for sequents whose formulae are endowed with a partial order. A proof net calculus, a quotient of the sequent calculus is defined in terms of directed graphs. This calculus enjoys a denotational semantics with coherence spaces, which is preserved under cut eliminatio, a terminating and confluent process. Some needed combinatorial properties of partial orders and proof graphs are established, as well as some properties of the commutative calculus with the MIX rule.</p>
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              <p>Cette thèse présente un calcul des séquents pour la logique linéaire enrichie d'un connecteur non commutatif et autodual "précède" situé entre le "par" et le "tenseur". Il est défini pour des séquents dont les formules sont orientées par un ordre partiel. Un calcul de réseaux de démonstration quotientant ce calcul des séquents est défini en termes de graphes orientés. Ce calcul est doté d'une sémantique dénotationnelle dans les espaces cohérents, préservée par élimination des coupures, un processus convergent et confluent. Des résultats combinatoires nécessaires sur les ordres partiels et sur la structure des graphes de démonstrations sont établies ainsi que quelques propriétés du calcul commutatif avec la règle MIX.</p>
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