逻辑信息模型（Logical Information Model） for Java：Example 18
逻辑信息模型（Logical Information Model） for Java：Example 18
"lim4j-samples": Example 18
sample代码如下：
public static void main(String[] args) throws Exception {
Argument a1 = new Argument("∵ax²+bx+c=0, ∴x=(-b±√(b²-4ac))/2a");
Argument a2 = new Argument("∵ax²+bx+c=0, ∴x²+(b/a)x+(c/a)=0");
Argument a3 = new Argument("∵x²+(b/a)x+(c/a)=0, ∴x²+2(b/2a)x+(b/2a)²=-(c/a)+(b/2a)²");
Argument a4 = new Argument("∵x²+2(b/2a)x+(b/2a)²=-(c/a)+(b/2a)², ∴(x+(b/2a))²=(b²-4ac)/4a²");
Argument a5 = new Argument("∵(x+(b/2a))²=(b²-4ac)/4a², ∴x+(b/2a)=√(b²-4ac)/2a");
Argument a6 = new Argument("∵x+(b/2a)=√(b²-4ac)/2a, ∴x=(-b±√(b²-4ac))/2a");
JudgedStatement js1 = new Definition("ax²+bx+c=0");
JudgedStatement js2 = new Definition("x=(-b±√(b²-4ac))/2a");
JudgedStatement js3 = new Definition("x²+(b/a)x+(c/a)=0");
JudgedStatement js4 = new Definition("x²+2(b/2a)x+(b/2a)²=-(c/a)+(b/2a)²");
JudgedStatement js5 = new Definition("(x+(b/2a))²=(b²-4ac)/4a²");
JudgedStatement js6 = new Definition("x+(b/2a)=±√(b²-4ac)/2a");
JudgedStatement js7 = new HypotheticalProposition("If ac=bc, and c≠0, then a=b. (cancellation law of multiplication)");
JudgedStatement js8 = new HypotheticalProposition("If a+c=b+c, then a=b. (cancellation law of addition)");
JudgedStatement js9 = new Definition("x²+2kx+k²=(x+k)², k∈R");
JudgedStatement js10 = new HypotheticalProposition("If a²=b², then a=±b.");
Condition cd1 = new Condition("a,b,c∈R, a≠0");
a2.addEvidence(js1, js7);
a2.addConclusion(js3);
a2.addCondition(cd1);
a2.setValidity(new Validity(1));
a3.addEvidence(js3, js8);
a3.addConclusion(js4);
a3.addCondition(cd1);
a3.setValidity(new Validity(1));
a4.addEvidence(js4, js9);
a4.addConclusion(js5);
a4.addCondition(cd1);
a4.setValidity(new Validity(1));
a5.addEvidence(js5, js10);
a5.addConclusion(js6);
a5.addCondition(cd1);
a5.setValidity(new Validity(1));
a6.addEvidence(js6, js8);
a6.addConclusion(js2);
a6.addCondition(cd1);
a6.setValidity(new Validity(1));
a1.addEvidence(js1);
a1.addConclusion(js2);
a1.addCondition(cd1);
a1.addSubArgument(a2, a3, a4, a5, a6);
a1.setValidity(new Validity(1));
Root root = new Root(a1);
root.marshalToXml(true, System.out);
}
输出结果：
∵ax²+bx+c=0, ∴x=(-b±√(b²-4ac))/2a
∵ax²+bx+c=0, ∴x²+(b/a)x+(c/a)=0
∵x²+(b/a)x+(c/a)=0, ∴x²+2(b/2a)x+(b/2a)²=-(c/a)+(b/2a)²
∵x²+2(b/2a)x+(b/2a)²=-(c/a)+(b/2a)², ∴(x+(b/2a))²=(b²-4ac)/4a²
∵(x+(b/2a))²=(b²-4ac)/4a², ∴x+(b/2a)=√(b²-4ac)/2a
∵x+(b/2a)=√(b²-4ac)/2a, ∴x=(-b±√(b²-4ac))/2a
ax²+bx+c=0
x=(-b±√(b²-4ac))/2a
x²+(b/a)x+(c/a)=0
x²+2(b/2a)x+(b/2a)²=-(c/a)+(b/2a)²
(x+(b/2a))²=(b²-4ac)/4a²
x+(b/2a)=±√(b²-4ac)/2a
If ac=bc, and c≠0, then a=b. (cancellation law of multiplication)
If a+c=b+c, then a=b. (cancellation law of addition)
x²+2kx+k²=(x+k)², k∈R
If a²=b², then a=±b.
a,b,c∈R, a≠0
VALID
VALID
VALID
VALID
VALID
VALID
=============================
源代码：
lim4j-samples：https://github.com/CodeJStudio/lim4j-samples
lim4j： https://github.com/CodeJStudio/lim4j
参考文献：
《逻辑信息模型与逻辑信息网络》 / "Theory of Logical Information Model & Logical Information Network"
《从逻辑信息模型，到逻辑信息网络，直至实现通用人工智能》