Název: Aspekty věty o eliminovatelnosti řezů
Překlad názvu: Aspects of the Cut-Elimination Theorem
Autoři: Rýdl, Jiří ; Švejdar, Vítězslav (vedoucí práce) ; Bílková, Marta (oponent)
Typ dokumentu: Bakalářské práce
Rok: 2021
Jazyk: eng
Abstrakt: [eng] [cze]
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]. 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)
Klíčová slova: pravidlo řezu|sekventový kalkulus|délky důkazů; cut rule|sequent calculus|lengths of proofs

Instituce: Fakulty UK (VŠKP) (web)
Informace o dostupnosti dokumentu: Dostupné v digitálním repozitáři UK.
Původní záznam: http://hdl.handle.net/20.500.11956/150414

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-452547


Záznam je zařazen do těchto sbírek:
Školství > Veřejné vysoké školy > Univerzita Karlova > Fakulty UK (VŠKP)
Vysokoškolské kvalifikační práce > Bakalářské práce