Osnove logike sudova

master's thesis

• Author: Petra Lucia Bakotić
• Mentor: Dijana Ilišević (mentor)
• Committee member: Dijana Ilišević (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Saša Singer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Temelji logike zapravo su i temelji matematike. Temelj logike je sud. Od brojnih vrsta sudova, matematičari su izabrali nekolicinu. Iz logičkih sudova izveli su logičke operacije. Pomoću logičkih operacija sudove su pretvorili u formule i stvorili takozvanu simboličku logiku. Time logika postaje matematička disciplina. Svaki sud ima svoju istinosnu vrijednost, koja se najlakše određuje pomoću semantičke tablice. U simboličkoj matematici više nije važan sadržaj suda, već njegova semantička vrijednost. Tako dva suda opisana različitim rečenicama mogu imati istu logičku formulu, odnosno istu semantičku vrijednost. Također, dva suda opisana različitim rečenicama mogu imati različitu logičku formulu, ali istu semantičku vrijednost. Takvi sudovi nazivaju se semantički jednakim sudovima. Sve matematičke definicije, aksiomi i teoremi logički su sudovi. Svaki teorem ima oblik implikacije. Prethodnik i sljedbenik te implikacije zapravo su pretpostavka i tvrdnja teorema. U dokazima teorema, osim implikacije koriste se i drugi sudovi, primjerice obrat implikacije i kontrapozicija.

Abstract (english)

Fundamentals of logic are also considered fundamentals of mathematics. Basic of logic is statement. Among many different types of statements, mathematicians have chosen few of them. They have derived logical operations from logical statements. Using logical operations they have converted statements into formulas, and in that way, made so called symbolic logic. Thereby, logic has become mathematical discipline. Every statement has its’ own value, which can be easily determined by semantic table. In symbolic mathematics, content of statement is replaced with semantic value. In that way, two statements which are described with different sentences can have the same logical formula or the same semantic value. Moreover, two statements described with different sentences can also have different logical formulas, but the same semantic value. Those statements are called semantically equal statements. All mathematical definitions, axioms and theorems, are logical statements. Every theorem has a form of implication. Predecessor and successor of implication are assumption and claim of theorem. In proofs of theorems, beside implication, we also use other statements like converse implication and contraposition.

• Keywords: logički sud; logičke operacije; simbolička logika; semantička tablica; semantička vrijednost
• Keywords (english): logical statement; logical operations; symbolic logic; semantic table; semantic value
• Language: croatian
• URN:NBN: urn:nbn:hr:217:425734
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2017-05-09 12:53:44