Lecture 1数理逻辑.pptVIP

导出规则 导出规则（Dr1,1,2,3,4,5,6） There are three suspects for a murder. Admas, Brown, and Clark. Admas says “I did not do it.The victim was an old acquaintance of Browns. But Clark hated him.” Brown states “I did not do it. I did not even know the guy. Besides I was out of town all that week.” Clark says “I did not do it. I saw both Admas and Brown downtown with the victim that day; one of them must have done it.” Assume that the two innocent men are telling truth, but that the guilty man might not be. Who did it? 导出规则 酿酒坛坛好做醋缸缸酸 养猪大于山老鼠只只亡 导出规则 酿酒坛坛好做醋，缸缸酸 养猪大于山老鼠，只只亡 导出规则 黄河远上白云间 一片孤城万仞山 羌笛何须怨杨柳 春风不渡玉门关 导出规则 黄河远上，白云间 一片，孤城万仞山。 羌笛何须怨，杨柳 春风，不渡玉门关。 形式系统 录取研究生(c)有许多条件：外语成绩不低于55分(a)，或者不及格科目不多于两门。 三种表达如下：如果外语成绩低于55分，并且不及格科目多于2门，那么不被录取。(not a and not b then not c) 如果某人未被录取研究生，那么他的外语成绩低于55分，或者不及格门数多于2门.(not c then not a or not b) 如果外语成绩低于55分，或者不及格门数多于2门，那么不被录取。((not a or not b) then not c) There are three suspects for a murder. Admas, Brown, and Clark. Admas says “I did not do it.The victim was an old acquaintance of Browns. But Clark hated him.” Brown states “I did not do it. I did not even know the guy. Besides I was out of town all that week.” Clark says “I did not do it. I saw both Admas and Brown downtown with the victim that day; one of them must have done it.” Assume that the two innocent men are telling truth, but that the guilty man might not be. Who did it? 一块陆地变成一个顶点，该问题可以变成以下图中寻找一条路径的问题 返回哥尼斯堡问题 * 形式系统 通常还要对FS加以限制，使得FS推演能够机械的实现 a. ∑为有穷集或者可数集 b. Term, Formula, Atom, Axiom, Rule都是递归的，即成员关系是可判定的 初等数论形式系统FSEN ∑={0,’,≈} Term={0,0’,0’’,…} Formula={t1≈t2 │t1,t2 ∈Term}=Atom Axiom= {0≈ 0} Rule={r}，其中，r={ t1≈t2, t1 ’ ≈t2 ’ │t1,t2 ∈Term} 初等代数中的群论形式系统FSG ∑= {e,*,-1,(,), ≈} ∪ X,其中，X为集合且X ∩ {e,*,-1,(,), ≈} = Φ Term= ，其中 T0=X ∪{e} Ti+1={(t-1),(t1*t2)│t,t1,t2 ∈ T i}i=0,1,.. Formula={t1≈t2 │t1,t2 ∈Term}=Atom Axiom= {a≈ a │a ∈X ∪{e}} ∪{et ≈t,t-1*t ≈e,(t1*t2)*t3 ≈t1*(t2*t3) │t1,t2,t3 ∈Term} 初等代数中的群论形式系统FSG Rule={r1