discretet mathmatics and its application1(이산수학 수업정리2)

Mathematic = Formal Language = logic

 

Language:

 

Purpose of language

     comunication

           - Expression of idea/imformation

           - Urder standing of expression

     A way of thinking

           -Represent your concept

           -Application of inference to reason

 

what are the components of language

      - Alphabet, Words, phrases(구), Sentence(statements), Paragraph(절)

 

what is the basic unit of communication/information

      - Sentence(statements)

 

learning languges?

 

Eg. English

• Expression
• understanding: reading/ compressio

 

 1. How to make proper sentence

-Syntax

 2. How to understand the meaning of the sentences

-Semantics

 

Logic

 

-Syntax(rule of making sentences: 구문법)

-Semantics(rule of understanding meaning of sentences 의미론)

 

Logics

-Proposition Logic(명제 논리)

-predicate logic(술어 논리),FOL(First- order Logic)

-Second- Order and beyond

      -Temperal logic

      -Modal logic

 

 

Propostional Logic

      -Syntax(How to make sentence) 

            - Make new proposion by combining proposition using operators

      -Semantics(How to understand/interprete the meaning of sentence/proposition)

                -How to assign truth value  (True/False) to a proposition

What is the proposition?

   - A proposition is a sentence that can be interpreted as either true of false

 

 

A is B

Operator is a function that has same type of inputs and an output

 

important slides!!!

condition -> F,  F / conclution -> T, T

logical equivalent