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master's thesis
Polimodalna logika dokazivosti GLP
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:789925
Matijašević, Ivo
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Matijašević, I. (2017). Polimodalna logika dokazivosti GLP (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:789925

Matijašević, Ivo. "Polimodalna logika dokazivosti GLP." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:789925

Matijašević, Ivo. "Polimodalna logika dokazivosti GLP." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:789925

Matijašević, I. (2017). 'Polimodalna logika dokazivosti GLP', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:789925

Matijašević I. Polimodalna logika dokazivosti GLP [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:789925

I. Matijašević, "Polimodalna logika dokazivosti GLP", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:789925

Metadata
TitlePolimodalna logika dokazivosti GLP
AuthorIvo Matijašević
MentorMladen Vuković (mentor)
Committee memberMladen Vuković (predsjednik povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu glavni cilj je dokazati topološku potpunost zatvorenog fragmenta polimodalne logike GLP. Definiramo logiku dokazivosti GL i takozvanu Kripkeovu semantiku za modalne logike koja uspostavlja vezu između relacijskih struktura i modalnog jezika. Ujedno definiramo aritmetičku interpretaciji logike dokazivosti te izričemo Solovayev prvi teorem aritmetičke potpunosti čiji se dokaz temelji na Kripkeovoj semantici za GL. Definiramo modalni sistem s beskonačno mnogo modalnih operatora, GLP, te dokazujemo nepotpunosti sistema GLP u odnosu na vlastitu Kripkeovu semantiku. Zatvoreni fragment sistema GLP, koji označavamo sa GLP\(_0\), ima odgovarajuću Kripkeovu semantiku u obliku takozvanog Ignatievog univerzalnog okvira. Taj okvir onda proširujemo tako da bude izomorfan kanonskom okviru i taj rezultat iskorištavamo kako bi definirali jednostavan topološki model nad ordinalnim brojem \(\epsilon_0\), na kojem je promatrana logika potpuna.
Abstract (english)
The main goal of this thesis is to show the closed fragment of polymodal logic GLP is complete with respect to a certain topological model. We define provability logic GL and so-called Kripke semantics for modal logics, which establishes a connection between relational structures and modal language. Also, we define the arithmetical interpretation of logic of provability and state Solovay’s first arithmetical completeness theorem, whose proof relies on Kripke semantics for GL. We define a model system with infinitely many modalities, GLP, and show that it is incomplete with respect to its class of Kripke frames. Closed fragment of system GLP, which we denote by GLP\(_0\), has appropriate semantics in the form of Ignatiev’s universal frame. That frame is then expanded to one that is isomorphic to the canonical frame and we use that result to define a simple topological model on the ordinal \(\epsilon_0\) for which we have completeness result.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:789925
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-02-28 12:28:48