Regaining cut admissibility in deduction modulo using abstract completion
Identifieur interne : 000232 ( PascalFrancis/Corpus ); précédent : 000231; suivant : 000233Regaining cut admissibility in deduction modulo using abstract completion
Auteurs : Guillaume Burel ; Claude KirchnerSource :
- Information and computation : (Print) [ 0890-5401 ] ; 2010.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore. We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system. Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth-Bendix completion in a non-trivial way, using the framework of abstract canonical systems. These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving.
Notice en format standard (ISO 2709)
Pour connaître la documentation sur le format Inist Standard.
pA |
|
---|
Format Inist (serveur)
NO : | PASCAL 10-0105560 INIST |
---|---|
ET : | Regaining cut admissibility in deduction modulo using abstract completion |
AU : | BUREL (Guillaume); KIRCHNER (Claude) |
AF : | Nancy-Université, Université Henri Poincaré, Faculté des sciences et techniques, Campus Victor Grignard, BP 70239/54506 Vandœuvre-lés-Nancy/France (1 aut.); INRIA, Centre de Recherche INRIA Bordeaux - Sud-Ouest, 351 cours de la Libération, Bâtiment A29/33405 Talence/France (2 aut.); LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239/54506 Vandœuvre-lés-Nancy/France (1 aut., 2 aut.) |
DT : | Publication en série; Niveau analytique |
SO : | Information and computation : (Print); ISSN 0890-5401; Coden INFCEC; Etats-Unis; Da. 2010; Vol. 208; No. 2; Pp. 140-164; Bibl. 39 ref. |
LA : | Anglais |
EA : | Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore. We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system. Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth-Bendix completion in a non-trivial way, using the framework of abstract canonical systems. These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving. |
CC : | 001D02A08; 001D02C02; 001D02A05 |
FD : | Admissibilité; Complétion; Preuve; Règle inférence; Calcul séquent; Congruence; Déploiement; Procédure; Puissance; Démonstration théorème; Réécriture; Relation ordre; Informatique théorique; Déduction naturelle; 68T15; 68Q42; Système deductif |
ED : | Admissibility; Completion; Proof; Inference rule; Sequent calculus; Congruence; Unfolding; Procedure; Power; Theorem proving; Rewriting; Ordering; Computer theory; Deductive system |
SD : | Admisibilidad; Compleción; Prueba; Regla inferencia; Càlculo sequente; Congruencia; Despliegue; Procedimiento; Potencia; Demostración teorema; Reescritura; Relación orden; Informática teórica |
LO : | INIST-8341.354000180885010030 |
ID : | 10-0105560 |
Links to Exploration step
Pascal:10-0105560Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Regaining cut admissibility in deduction modulo using abstract completion</title>
<author><name sortKey="Burel, Guillaume" sort="Burel, Guillaume" uniqKey="Burel G" first="Guillaume" last="Burel">Guillaume Burel</name>
<affiliation><inist:fA14 i1="01"><s1>Nancy-Université, Université Henri Poincaré, Faculté des sciences et techniques, Campus Victor Grignard, BP 70239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
</affiliation>
<affiliation><inist:fA14 i1="03"><s1>LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
<author><name sortKey="Kirchner, Claude" sort="Kirchner, Claude" uniqKey="Kirchner C" first="Claude" last="Kirchner">Claude Kirchner</name>
<affiliation><inist:fA14 i1="02"><s1>INRIA, Centre de Recherche INRIA Bordeaux - Sud-Ouest, 351 cours de la Libération, Bâtiment A29</s1>
<s2>33405 Talence</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
<affiliation><inist:fA14 i1="03"><s1>LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">INIST</idno>
<idno type="inist">10-0105560</idno>
<date when="2010">2010</date>
<idno type="stanalyst">PASCAL 10-0105560 INIST</idno>
<idno type="RBID">Pascal:10-0105560</idno>
<idno type="wicri:Area/PascalFrancis/Corpus">000232</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Regaining cut admissibility in deduction modulo using abstract completion</title>
<author><name sortKey="Burel, Guillaume" sort="Burel, Guillaume" uniqKey="Burel G" first="Guillaume" last="Burel">Guillaume Burel</name>
<affiliation><inist:fA14 i1="01"><s1>Nancy-Université, Université Henri Poincaré, Faculté des sciences et techniques, Campus Victor Grignard, BP 70239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
</affiliation>
<affiliation><inist:fA14 i1="03"><s1>LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
<author><name sortKey="Kirchner, Claude" sort="Kirchner, Claude" uniqKey="Kirchner C" first="Claude" last="Kirchner">Claude Kirchner</name>
<affiliation><inist:fA14 i1="02"><s1>INRIA, Centre de Recherche INRIA Bordeaux - Sud-Ouest, 351 cours de la Libération, Bâtiment A29</s1>
<s2>33405 Talence</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
<affiliation><inist:fA14 i1="03"><s1>LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</inist:fA14>
</affiliation>
</author>
</analytic>
<series><title level="j" type="main">Information and computation : (Print)</title>
<title level="j" type="abbreviated">Inf. comput. : (Print)</title>
<idno type="ISSN">0890-5401</idno>
<imprint><date when="2010">2010</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><title level="j" type="main">Information and computation : (Print)</title>
<title level="j" type="abbreviated">Inf. comput. : (Print)</title>
<idno type="ISSN">0890-5401</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Admissibility</term>
<term>Completion</term>
<term>Computer theory</term>
<term>Congruence</term>
<term>Deductive system</term>
<term>Inference rule</term>
<term>Ordering</term>
<term>Power</term>
<term>Procedure</term>
<term>Proof</term>
<term>Rewriting</term>
<term>Sequent calculus</term>
<term>Theorem proving</term>
<term>Unfolding</term>
</keywords>
<keywords scheme="Pascal" xml:lang="fr"><term>Admissibilité</term>
<term>Complétion</term>
<term>Preuve</term>
<term>Règle inférence</term>
<term>Calcul séquent</term>
<term>Congruence</term>
<term>Déploiement</term>
<term>Procédure</term>
<term>Puissance</term>
<term>Démonstration théorème</term>
<term>Réécriture</term>
<term>Relation ordre</term>
<term>Informatique théorique</term>
<term>Déduction naturelle</term>
<term>68T15</term>
<term>68Q42</term>
<term>Système deductif</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore. We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system. Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth-Bendix completion in a non-trivial way, using the framework of abstract canonical systems. These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving.</div>
</front>
</TEI>
<inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0890-5401</s0>
</fA01>
<fA02 i1="01"><s0>INFCEC</s0>
</fA02>
<fA03 i2="1"><s0>Inf. comput. : (Print)</s0>
</fA03>
<fA05><s2>208</s2>
</fA05>
<fA06><s2>2</s2>
</fA06>
<fA08 i1="01" i2="1" l="ENG"><s1>Regaining cut admissibility in deduction modulo using abstract completion</s1>
</fA08>
<fA11 i1="01" i2="1"><s1>BUREL (Guillaume)</s1>
</fA11>
<fA11 i1="02" i2="1"><s1>KIRCHNER (Claude)</s1>
</fA11>
<fA14 i1="01"><s1>Nancy-Université, Université Henri Poincaré, Faculté des sciences et techniques, Campus Victor Grignard, BP 70239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</fA14>
<fA14 i1="02"><s1>INRIA, Centre de Recherche INRIA Bordeaux - Sud-Ouest, 351 cours de la Libération, Bâtiment A29</s1>
<s2>33405 Talence</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</fA14>
<fA14 i1="03"><s1>LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239</s1>
<s2>54506 Vandœuvre-lés-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
<sZ>2 aut.</sZ>
</fA14>
<fA20><s1>140-164</s1>
</fA20>
<fA21><s1>2010</s1>
</fA21>
<fA23 i1="01"><s0>ENG</s0>
</fA23>
<fA43 i1="01"><s1>INIST</s1>
<s2>8341</s2>
<s5>354000180885010030</s5>
</fA43>
<fA44><s0>0000</s0>
<s1>© 2010 INIST-CNRS. All rights reserved.</s1>
</fA44>
<fA45><s0>39 ref.</s0>
</fA45>
<fA47 i1="01" i2="1"><s0>10-0105560</s0>
</fA47>
<fA60><s1>P</s1>
</fA60>
<fA61><s0>A</s0>
</fA61>
<fA64 i1="01" i2="1"><s0>Information and computation : (Print)</s0>
</fA64>
<fA66 i1="01"><s0>USA</s0>
</fA66>
<fC01 i1="01" l="ENG"><s0>Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore. We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system. Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth-Bendix completion in a non-trivial way, using the framework of abstract canonical systems. These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving.</s0>
</fC01>
<fC02 i1="01" i2="X"><s0>001D02A08</s0>
</fC02>
<fC02 i1="02" i2="X"><s0>001D02C02</s0>
</fC02>
<fC02 i1="03" i2="X"><s0>001D02A05</s0>
</fC02>
<fC03 i1="01" i2="X" l="FRE"><s0>Admissibilité</s0>
<s5>17</s5>
</fC03>
<fC03 i1="01" i2="X" l="ENG"><s0>Admissibility</s0>
<s5>17</s5>
</fC03>
<fC03 i1="01" i2="X" l="SPA"><s0>Admisibilidad</s0>
<s5>17</s5>
</fC03>
<fC03 i1="02" i2="X" l="FRE"><s0>Complétion</s0>
<s5>18</s5>
</fC03>
<fC03 i1="02" i2="X" l="ENG"><s0>Completion</s0>
<s5>18</s5>
</fC03>
<fC03 i1="02" i2="X" l="SPA"><s0>Compleción</s0>
<s5>18</s5>
</fC03>
<fC03 i1="03" i2="X" l="FRE"><s0>Preuve</s0>
<s5>19</s5>
</fC03>
<fC03 i1="03" i2="X" l="ENG"><s0>Proof</s0>
<s5>19</s5>
</fC03>
<fC03 i1="03" i2="X" l="SPA"><s0>Prueba</s0>
<s5>19</s5>
</fC03>
<fC03 i1="04" i2="X" l="FRE"><s0>Règle inférence</s0>
<s5>20</s5>
</fC03>
<fC03 i1="04" i2="X" l="ENG"><s0>Inference rule</s0>
<s5>20</s5>
</fC03>
<fC03 i1="04" i2="X" l="SPA"><s0>Regla inferencia</s0>
<s5>20</s5>
</fC03>
<fC03 i1="05" i2="X" l="FRE"><s0>Calcul séquent</s0>
<s5>21</s5>
</fC03>
<fC03 i1="05" i2="X" l="ENG"><s0>Sequent calculus</s0>
<s5>21</s5>
</fC03>
<fC03 i1="05" i2="X" l="SPA"><s0>Càlculo sequente</s0>
<s5>21</s5>
</fC03>
<fC03 i1="06" i2="X" l="FRE"><s0>Congruence</s0>
<s5>22</s5>
</fC03>
<fC03 i1="06" i2="X" l="ENG"><s0>Congruence</s0>
<s5>22</s5>
</fC03>
<fC03 i1="06" i2="X" l="SPA"><s0>Congruencia</s0>
<s5>22</s5>
</fC03>
<fC03 i1="07" i2="X" l="FRE"><s0>Déploiement</s0>
<s5>23</s5>
</fC03>
<fC03 i1="07" i2="X" l="ENG"><s0>Unfolding</s0>
<s5>23</s5>
</fC03>
<fC03 i1="07" i2="X" l="SPA"><s0>Despliegue</s0>
<s5>23</s5>
</fC03>
<fC03 i1="08" i2="X" l="FRE"><s0>Procédure</s0>
<s5>24</s5>
</fC03>
<fC03 i1="08" i2="X" l="ENG"><s0>Procedure</s0>
<s5>24</s5>
</fC03>
<fC03 i1="08" i2="X" l="SPA"><s0>Procedimiento</s0>
<s5>24</s5>
</fC03>
<fC03 i1="09" i2="X" l="FRE"><s0>Puissance</s0>
<s5>25</s5>
</fC03>
<fC03 i1="09" i2="X" l="ENG"><s0>Power</s0>
<s5>25</s5>
</fC03>
<fC03 i1="09" i2="X" l="SPA"><s0>Potencia</s0>
<s5>25</s5>
</fC03>
<fC03 i1="10" i2="X" l="FRE"><s0>Démonstration théorème</s0>
<s5>26</s5>
</fC03>
<fC03 i1="10" i2="X" l="ENG"><s0>Theorem proving</s0>
<s5>26</s5>
</fC03>
<fC03 i1="10" i2="X" l="SPA"><s0>Demostración teorema</s0>
<s5>26</s5>
</fC03>
<fC03 i1="11" i2="X" l="FRE"><s0>Réécriture</s0>
<s5>27</s5>
</fC03>
<fC03 i1="11" i2="X" l="ENG"><s0>Rewriting</s0>
<s5>27</s5>
</fC03>
<fC03 i1="11" i2="X" l="SPA"><s0>Reescritura</s0>
<s5>27</s5>
</fC03>
<fC03 i1="12" i2="X" l="FRE"><s0>Relation ordre</s0>
<s5>28</s5>
</fC03>
<fC03 i1="12" i2="X" l="ENG"><s0>Ordering</s0>
<s5>28</s5>
</fC03>
<fC03 i1="12" i2="X" l="SPA"><s0>Relación orden</s0>
<s5>28</s5>
</fC03>
<fC03 i1="13" i2="X" l="FRE"><s0>Informatique théorique</s0>
<s5>29</s5>
</fC03>
<fC03 i1="13" i2="X" l="ENG"><s0>Computer theory</s0>
<s5>29</s5>
</fC03>
<fC03 i1="13" i2="X" l="SPA"><s0>Informática teórica</s0>
<s5>29</s5>
</fC03>
<fC03 i1="14" i2="X" l="FRE"><s0>Déduction naturelle</s0>
<s4>INC</s4>
<s5>70</s5>
</fC03>
<fC03 i1="15" i2="X" l="FRE"><s0>68T15</s0>
<s4>INC</s4>
<s5>71</s5>
</fC03>
<fC03 i1="16" i2="X" l="FRE"><s0>68Q42</s0>
<s4>INC</s4>
<s5>72</s5>
</fC03>
<fC03 i1="17" i2="X" l="FRE"><s0>Système deductif</s0>
<s4>CD</s4>
<s5>96</s5>
</fC03>
<fC03 i1="17" i2="X" l="ENG"><s0>Deductive system</s0>
<s4>CD</s4>
<s5>96</s5>
</fC03>
<fN21><s1>067</s1>
</fN21>
<fN44 i1="01"><s1>OTO</s1>
</fN44>
<fN82><s1>OTO</s1>
</fN82>
</pA>
</standard>
<server><NO>PASCAL 10-0105560 INIST</NO>
<ET>Regaining cut admissibility in deduction modulo using abstract completion</ET>
<AU>BUREL (Guillaume); KIRCHNER (Claude)</AU>
<AF>Nancy-Université, Université Henri Poincaré, Faculté des sciences et techniques, Campus Victor Grignard, BP 70239/54506 Vandœuvre-lés-Nancy/France (1 aut.); INRIA, Centre de Recherche INRIA Bordeaux - Sud-Ouest, 351 cours de la Libération, Bâtiment A29/33405 Talence/France (2 aut.); LORIA, Équipe Pareo, Bâtiment B, Campus Scientifique, BP239/54506 Vandœuvre-lés-Nancy/France (1 aut., 2 aut.)</AF>
<DT>Publication en série; Niveau analytique</DT>
<SO>Information and computation : (Print); ISSN 0890-5401; Coden INFCEC; Etats-Unis; Da. 2010; Vol. 208; No. 2; Pp. 140-164; Bibl. 39 ref.</SO>
<LA>Anglais</LA>
<EA>Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore. We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system. Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth-Bendix completion in a non-trivial way, using the framework of abstract canonical systems. These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving.</EA>
<CC>001D02A08; 001D02C02; 001D02A05</CC>
<FD>Admissibilité; Complétion; Preuve; Règle inférence; Calcul séquent; Congruence; Déploiement; Procédure; Puissance; Démonstration théorème; Réécriture; Relation ordre; Informatique théorique; Déduction naturelle; 68T15; 68Q42; Système deductif</FD>
<ED>Admissibility; Completion; Proof; Inference rule; Sequent calculus; Congruence; Unfolding; Procedure; Power; Theorem proving; Rewriting; Ordering; Computer theory; Deductive system</ED>
<SD>Admisibilidad; Compleción; Prueba; Regla inferencia; Càlculo sequente; Congruencia; Despliegue; Procedimiento; Potencia; Demostración teorema; Reescritura; Relación orden; Informática teórica</SD>
<LO>INIST-8341.354000180885010030</LO>
<ID>10-0105560</ID>
</server>
</inist>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/PascalFrancis/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000232 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/PascalFrancis/Corpus/biblio.hfd -nk 000232 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= PascalFrancis |étape= Corpus |type= RBID |clé= Pascal:10-0105560 |texte= Regaining cut admissibility in deduction modulo using abstract completion }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |