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master's thesis
Lindströmov teorem za modalnu logiku
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:499656
Krunić, Jakov
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Krunić, J. (2020). Lindströmov teorem za modalnu logiku (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:499656

Krunić, Jakov. "Lindströmov teorem za modalnu logiku." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:499656

Krunić, Jakov. "Lindströmov teorem za modalnu logiku." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:499656

Krunić, J. (2020). 'Lindströmov teorem za modalnu logiku', Master's thesis, University of Zagreb, Faculty of Science, accessed 02 July 2024, https://urn.nsk.hr/urn:nbn:hr:217:499656

Krunić J. Lindströmov teorem za modalnu logiku [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 July 02] Available at: https://urn.nsk.hr/urn:nbn:hr:217:499656

J. Krunić, "Lindströmov teorem za modalnu logiku", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:499656

Metadata
TitleLindströmov teorem za modalnu logiku
AuthorJakov Krunić
MentorMladen Vuković (mentor)
MentorTin Perkov (sumentor)
Committee memberMladen Vuković (predsjednik povjerenstva)
Committee memberTin Perkov (član povjerenstva)
Committee memberVedran Čačić (član povjerenstva)
Committee memberMarko Horvat (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-07-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Lindströmovi teoremi karakteriziraju logiku prvog reda i predstavljaju temelj apstraktne teorije modela. Oni osiguravaju posebno mjesto logici prvog reda među svim logičkim sustavima. U ovom diplomskog radu prikazuju se analogni rezultati u kontekstu modalnih logika. Najvažniji pojam koji proučavamo jest apstraktna modalna logika. Glavni cilj ovog diplomskog rada je dokazati analogon Lindströmovog teorema o karakterizaciji modalnih logika. Rad je podijeljen u dva poglavlja. Cilj prvog poglavlja je opisati neke modalne sisteme. Najprije se bavimo sintaksom i semantikom modalne logike. Zatim uvodimo pojam osnovne modalne logike. Proučavamo generirane podmodele i bisimulacije te navodimo njihova svojstva. Nakon toga opisujemo dvije poznate modalne logike: propozicionalnu dinamičku logiku i linearnu temporalnu logiku. U drugom poglavlju definiramo pojmove apstraktne modalne logike i proširenja osnovne modalne logike. Zatim uvodimo apstraktne modalne logike konačnog stupnja. Detaljno dokazujemo Lindströmov teorem za modalnu logiku koji kaže da je osnovna modalna logika najjača apstraktna modalna logika konačnog stupnja. Na kraju navodimo i varijantu Lindströmovog teorema za modalnu logiku koristeći pojmove relativizacije i kompaktnosti..
Abstract (english)
Lindström's theorems characterize first-order logic and form the basis of abstract model theory. They provide a special place for first-order logic among all logical systems. This thesis presents analogous results in the context of modal logics. The most important concept we study is abstract modal logic. The main goal of this thesis is to prove an analogue of Lindström's theorem on the characterization of modal logics. The paper is divided into two chapters. The aim of the first chapter is to describe some modal systems. We first deal with the syntax and semantics of modal logic. Then we introduce the notion of basic modal logic. We study the generated submodels and bisimulations and list their properties. We then describe two known modal logics: propositional dynamic logic and linear temporal logic. In the second chapter, we define the concepts of abstract modal logic and extensions of basic modal logic. We then introduce abstract modal logics of finite degree. We prove in detail Lindström's theorem for modal logic which says that basic modal logic is the strongest abstract modal logic of finite degree. Finally, we list a variant of Lindström's theorem for modal logic using the terms relativization and compactness.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:499656
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 on2020-11-25 13:53:36