Formalni sistemi za dokazivanje teorema incidencije / Formal systems for proving incidence results

Description

<p>U ovoj tezi razvijen je formalni sistem za dokazivanje teorema<br />incidencije u projektivnoj geometiji. Osnova sistema je Čeva/Menelaj<br />metod za dokazivanje teorema incidencije. Formalizacija o kojoj je<br />ovdje riječ izvedena je korišćenjem &Delta;-kompleksa, pa su tako u<br />disertaciji spojene oblasti logike, geometrije i algebarske<br />topologije. Aksiomatski sekventi proizilaze iz 2-ciklova &Delta;-kompleksa.<br />Definisana je Euklidska i projektivna interpretacija sekvenata i<br />dokazana je saglasnost i odlučivost sistema. Dati su primjeri<br />iščitavanja teorema incidencije iz dokazivih sekvenata sistema. U<br />tezi je data i procedura za provjeru da li je skup od n šestorki tačaka<br />aksiomatski sekvent.</p> / <p>In this thesis, a formal sequent system for proving incidence theorems in<br />projective geometry is introduced. This system is based on the<br />Ceva/Menelaus method for proving theorems. This formalization is performed<br />using &Delta;-complexes, so the areas of logic, geometry and algebraic topology<br />are combined in the dissertation. The axiomatic sequents of the system stem<br />from 2-cycles of &Delta;-complexes. The Euclidean and projective interpretations of<br />the sequents are defined and the decidability and soundness of the system<br />are proved. Patterns for extracting formulation and proof of the incidence<br />result from derivable sequents of system are exemplified. The procedure for<br />deciding if set of n sextuples represent an axiomatic sequent is presented<br />within the thesis.</p>

Links & Downloads

1. https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija159480060455857.pdf?controlNumber=(BISIS)114829&fileName=159480060455857.pdf&id=16102&source=NDLTD&language=en
2. https://www.cris.uns.ac.rs/record.jsf?recordId=114829&source=NDLTD&language=en

Tags

Additional Fields

Identifer	oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)114829
Date	28 October 2020
Creators	Milićević Marina
Contributors	Petrić Zoran, Baralić Đorđe, Gilezan Silvia, Janičić Predrag, Doroslovački Ksenija
Publisher	Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, University of Novi Sad, Faculty of Technical Sciences at Novi Sad
Source Sets	University of Novi Sad
Language	Serbian
Detected Language	English
Type	PhD thesis