Kripke语义:可以使用学习软件吗? [英] Kripke semantics: learning software available?

查看：97 发布时间：2020/5/3 8:58:02 logic boolean-logic reasoning modal-logic

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问题描述

我被困在 Kripke语义上，想知道是否有educational software可供我使用可以测试语句的等效性，因为Im开始认为通过示例(即使是抽象变量)更容易学习.

I am stuck on Kripke semantics, and wonder if there is educational software through which I can test equivalence of statements etc, since Im starting to think its easier to learn by example (even if on abstract variables).

我会用

☐A必写A
♢A可能是A

☐真，☐假，♢真，♢假是否对值求值，如果是，则从什么集合({true，false}或{必要，可能})中获取什么值或种类的值? [1]

do ☐true, ☐false, ♢true, ♢false evaluate to values, if so what values or kinds of values from what set ({true, false} or perhaps {necessary,possibly})? [1]

我想我阅读了所有Kripke models并使用duality axiom:

I think I read all Kripke models use the duality axiom:

(☐A)->(¬♢¬ A)

(☐A)->(¬♢¬A)

即如果必须paytax，则不允许它不paytax
(无论是否需要纳税...)

i.e. if its necessary to paytax then its not allowed to not paytax
(irrespective of wheither its necessary to pay tax...)

即2.如果必须earnmoney则不允许earnmoney
(同样，到目前为止，无论是否真的需要赚钱，逻辑都成立)

i.e.2. if its necessary to earnmoney its not allowed to not earnmoney
(again irrespective of wheither earning money is really necessary, the logic holds, so far)

因为A-> B等同于¬ A<-¬ B可以测试

since A->B is equivalent to ¬A<-¬B lets test

¬☐A<-♢¬ A

¬☐A<-♢¬A

如果不允许upvote

此公理具有双重作用:

♢A->¬☐¬ A

♢A->¬☐¬A

如果允许earnmoney，则不必earnmoney

并非所有模态的行为都相同，并且不同的Kripke model更适合为一个模态建模，而不是另一种模型:并非所有的Kripke models都使用相同的axioms. (古典量词也是模态吗?如果可以，Kripke models可以对它们进行建模吗?)

Not all modalities behave the same, and different Kripke model are more suitable to model one modalit than another: not all Kripke models use the same axioms. (Are classical quantifiers also modalities? if so do Kripke models allow modeling them?)

我将浏览常见公理的列表，并尝试找到一些使假设似乎违反直觉或不必要的例子……

I will go through the list of common axioms and try to find examples that make it seem counterintuitive or unnecessary to postulate...

☐(A-> B)->(☐A->☐B):

如果((赚钱表示应纳税)是必要的) 然后((赚钱的必要性)意味着(纳税额的必要性))

if (its necessary that (earningmoney implies payingtaxes)) then ((necessity of earningmoney) implies (necessity of payingtaxes))

请注意，赚钱并不意味着要纳税，隐含的A-> B并不影响公理的真值...

note that earning money does not imply paying taxes, the falsehood of the implication A->B does not affect the truth value of the axiom...

力求花很长时间来表达我的问题以试图理解所有内容...随时进行编辑

urgh its taking too long to phrase my problems in trying to understand it all... feel free to edit

Kripke语义:可以使用学习软件吗? [英] Kripke semantics: learning software available?

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Kripke语义:可以使用学习软件吗? [英] Kripke semantics: learning software available?

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