Discrete mathematics Yi li Software sc Fudan unive April 18, 2012
Discrete Mathematics Yi Li Software School Fudan University April 18, 2012 Yi Li (Fudan University) Discrete Mathematics April 18, 2012 1 / 17
Review Atomic tableaux o CsT and properties
Review Atomic tableaux CST and properties Yi Li (Fudan University) Discrete Mathematics April 18, 2012 2 / 17
utline Syntax and semantics Soundness theorem o Completeness theorem
Outline Syntax and semantics Soundness theorem Completeness theorem Yi Li (Fudan University) Discrete Mathematics April 18, 2012 3 / 17
Syntax Semantics Example Give you two Chinese characters"更衣”, what's it mean? o It means change clothes in modern Chinese o It means go to washroom in ancient chinese Example Give an acronym "P", what's it mean? o Internet protocol in networl o Integer Programming in operation research o Interactive proof in complexity
Syntax & Semantics Example Give you two Chinese characters ”➁➓”, what’s it mean? It means change clothes in modern Chinese. It means go to washroom in ancient Chinese. Example Give an acronym ”IP”, what’s it mean? Internet Protocol in network. Integer Programming in operation research. Interactive proof in complexity. Yi Li (Fudan University) Discrete Mathematics April 18, 2012 4 / 17
Syntax Semantics am dle Give you the following programming segments O in C, printf("Hello World! ") O in Java, system. print("Hello World! " o in C++, cout<< Hello World! All of them just output"hello World! " on the screen
Syntax & Semantics Example Give you the following programming segments: 1 in C, printf(”Hello World!”); 2 in Java, system.print(”Hello World!”); 3 in C++, cout<<”Hello World!”; All of them just output ”Hello World!” on the screen. Yi Li (Fudan University) Discrete Mathematics April 18, 2012 5 / 17