dc.contributor.advisor | Švejdar, Vítězslav | |
dc.creator | Rýdl, Jiří | |
dc.date.accessioned | 2022-04-12T08:35:01Z | |
dc.date.available | 2022-04-12T08:35:01Z | |
dc.date.issued | 2021 | |
dc.identifier.uri | http://hdl.handle.net/20.500.11956/150414 | |
dc.description.abstract | I give a proof of the cut-elimination theorem (Gentzen's Hauptsatz) for an intuitionistic multi-succedent calculus. The proof follows the strategy of eliminating topmost maximal-rank cuts that allows for a straightforward way to measure the upper bound of the increase of derivations during the procedure. The elimination of all cut inferences generates a superexponential increase. I follow the structure of the proof for classical logic given in Švejdar's [18], modifying only the critical cases related to two restricted rules. Motivated by the diversity found in the early literature on this topic, I survey selected aspects of various formulations of sequent calculi. These are reflected in the proof of the Hauptsatz and its preliminaries. In the end I give one corollary of cut elimination, the Midsequent theorem, which is one of the three applications to be found already in Gentzen's [10]. Powered by TCPDF (www.tcpdf.org) | cs_CZ |
dc.description.abstract | I give a proof of the cut-elimination theorem (Gentzen's Hauptsatz ) for an intuitionistic multi-succedent calculus. The proof follows the strategy of eliminating topmost maximal-rank cuts that allows for a straightforward way to measure the upper bound of the increase of derivations during the procedure. The elimination of all cut inferences generates a superexponential increase. I follow the structure of the proof for classical logic given in Švejdar's [18], modifying only the critical cases related to two restricted rules. Motivated by the diversity found in the early literature on this topic, I survey selected aspects of various formulations of sequent calculi. These are reflected in the proof of the Hauptsatz and its preliminaries. In the end I give one corollary of cut elimination, the Midsequent theorem, which is one of the three applications to be found already in Gentzen's [10]. | en_US |
dc.language | English | cs_CZ |
dc.language.iso | en_US | |
dc.publisher | Univerzita Karlova, Filozofická fakulta | cs_CZ |
dc.subject | cut rule|sequent calculus|lengths of proofs | en_US |
dc.subject | pravidlo řezu|sekventový kalkulus|délky důkazů | cs_CZ |
dc.title | Aspects of the Cut-Elimination Theorem | en_US |
dc.type | bakalářská práce | cs_CZ |
dcterms.created | 2021 | |
dcterms.dateAccepted | 2021-09-07 | |
dc.description.department | Department of Logic | en_US |
dc.description.department | Katedra logiky | cs_CZ |
dc.description.faculty | Faculty of Arts | en_US |
dc.description.faculty | Filozofická fakulta | cs_CZ |
dc.identifier.repId | 232267 | |
dc.title.translated | Aspekty věty o eliminovatelnosti řezů | cs_CZ |
dc.contributor.referee | Bílková, Marta | |
thesis.degree.name | Bc. | |
thesis.degree.level | bakalářské | cs_CZ |
thesis.degree.discipline | Logika | cs_CZ |
thesis.degree.discipline | Logic | en_US |
thesis.degree.program | Logika | cs_CZ |
thesis.degree.program | Logic | en_US |
uk.thesis.type | bakalářská práce | cs_CZ |
uk.taxonomy.organization-cs | Filozofická fakulta::Katedra logiky | cs_CZ |
uk.taxonomy.organization-en | Faculty of Arts::Department of Logic | en_US |
uk.faculty-name.cs | Filozofická fakulta | cs_CZ |
uk.faculty-name.en | Faculty of Arts | en_US |
uk.faculty-abbr.cs | FF | cs_CZ |
uk.degree-discipline.cs | Logika | cs_CZ |
uk.degree-discipline.en | Logic | en_US |
uk.degree-program.cs | Logika | cs_CZ |
uk.degree-program.en | Logic | en_US |
thesis.grade.cs | Výborně | cs_CZ |
thesis.grade.en | Excellent | en_US |
uk.abstract.cs | I give a proof of the cut-elimination theorem (Gentzen's Hauptsatz) for an intuitionistic multi-succedent calculus. The proof follows the strategy of eliminating topmost maximal-rank cuts that allows for a straightforward way to measure the upper bound of the increase of derivations during the procedure. The elimination of all cut inferences generates a superexponential increase. I follow the structure of the proof for classical logic given in Švejdar's [18], modifying only the critical cases related to two restricted rules. Motivated by the diversity found in the early literature on this topic, I survey selected aspects of various formulations of sequent calculi. These are reflected in the proof of the Hauptsatz and its preliminaries. In the end I give one corollary of cut elimination, the Midsequent theorem, which is one of the three applications to be found already in Gentzen's [10]. Powered by TCPDF (www.tcpdf.org) | cs_CZ |
uk.abstract.en | I give a proof of the cut-elimination theorem (Gentzen's Hauptsatz ) for an intuitionistic multi-succedent calculus. The proof follows the strategy of eliminating topmost maximal-rank cuts that allows for a straightforward way to measure the upper bound of the increase of derivations during the procedure. The elimination of all cut inferences generates a superexponential increase. I follow the structure of the proof for classical logic given in Švejdar's [18], modifying only the critical cases related to two restricted rules. Motivated by the diversity found in the early literature on this topic, I survey selected aspects of various formulations of sequent calculi. These are reflected in the proof of the Hauptsatz and its preliminaries. In the end I give one corollary of cut elimination, the Midsequent theorem, which is one of the three applications to be found already in Gentzen's [10]. | en_US |
uk.file-availability | V | |
uk.grantor | Univerzita Karlova, Filozofická fakulta, Katedra logiky | cs_CZ |
thesis.grade.code | 1 | |
uk.publication-place | Praha | cs_CZ |
uk.thesis.defenceStatus | O | |