1、* 1Propositional LogicThree tasks1. What is a proposition?2. Translate natural languages into logical expression. 3. How to make a truth table? * 2* 3Proposition Proposition (statement)A declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both. Truth
2、 value:The value (result) of the proposition(真值，是命题最重要的属性 ）One of the element from set True, False* 4More Examples of Proposition Do you speak English?-This is a question, not a statement. 这个人太有才了！ Lets go! 我们要努力学习。 Teenagers shouldnt indulge in game.- It is not a statement, but an advice. 2+2=5结论：疑
3、问句、感叹句和祈使句都不是命题* 5More Examples of Proposition 3-x=5. x is a variable, so the truth value of this sentence is open. 这盘菜很咸。 这个人个很高。结论：聪明的你如果给不出真值那就不是命题* 6More Examples of Proposition有两个特例需要记住：1. 未来命题真值会水落石出的我们认为是命题 10年之后你一定是千万富翁。 火星上有生命2. 悖论 我正在说谎 我专门为不为自己理发的人理发* 7Propositional Variable A proposition
4、 can be represented by a proposition variable A propositional variable is often denoted as p, q, r, etc. e.g. p: Today is Tuesday. q: 2+2=4r: 2+3=6* 8Logical Connectives A simple statement can be represented by an atom proposition. More than one atom propositions can be combined into a compound stat
5、ement. The combination is achieved using “connectives”. Usually, the connective roughly corresponds some conjunctive in the natural language.* 9Negationp(also denoted by : it is not the case that pp pTFFTTruth table for p All possible value of p* 10否定联结词 Conectives:非不例：他说的并非都是对的。太原是一个不大的城市。太原并不是一个大城市。
