Say I have a sentence : If I water my plants then they will grow.
Would tenses have anything to do with writing it's negation and contraposition
Negation: I watered my plants but they did not grow.
Contrapositive: If they do not grow then I did not water my plants.
Best Answer
Classical logic (Logic from more than a thousand years ago) does not include notions of time (past, present, future, etc...).
The following are examples of a few rules of inference from classical logic:
Rule of Inference: Implication Operator From Parent to Left Child
Rule of Inference: Implication Operator From Parent to Right Child
Rule of Inference: DeMorgan's Law
Note that none of the rules of inference in classical logic talk about time.
It is not easy to express any of the following English sentences in logic from hundreds of years ago:
I would stay that it is incorrect to use classical logic to express the English sentence "If I water my plants then they will grow" as "$\mathtt{if}\, P \,\, \mathtt{then} \,\, Q$" where $P$ is "
I water my plants
"Even an operation as simple as negation is not the same in English as it is in classical logic.
Perhaps, you would say that the following are equivalent:
I do water my plants
I do
$\mathtt{NOT}$water my plants
The statements about plants might be okay. However, consider the two following two statements:
My wife's cousin Hector's pet monkey does like to eat strawberries
My wife's cousin Hector's pet monkey does
$\mathtt{NOT}$like to eat strawberries
There are some issues, not the least of which are:
In English, you are not allowed to move the word "$\mathtt{NOT}$" further and further to the left, or further to the right.
It is helpful to learn simple logic from ye olden days before you learn more advanced contemporary logic. However, I really wish that your teacher would not give you examples in English. English is really too complicated to force into the classical logic model.
In mathematics, time is sometimes modeled as follows:
If there exists at least one time in the future at which statement $P$ is true, then we write:
For example:
I still think that this is an abuse of the English language. However, using the symbols ◇ and □ to say something about time makes for a better model of English, relatively speaking, than using classical logic alone.
If something is true for all times in the future then we might write:
For example:
I am not sure that modal logic using the symbols ◇ and □ is great for English, but it does help in math sometimes.
For example, the following are equivalent:
Suppose that:
Well then, we have:
I water my plants
$\mathtt{THEN}$they will grow
I water my plants
) $\mathtt{AND}$ ($\mathtt{NOT} \,$they will grow
)they will grow
) $\mathtt{THEN} \text{ }$ ($\mathtt{NOT} \,\, \text{ }$I water my plants
)If some of the things written in the table above do not sound like English it is because, the things written in the table are not English.
You cannot model English sentences so easily using classical logic.
In English, the following two sentences have the same meaning:
With classical logic alone, you are not allowed to do something as simple as understand that the word "they" can be replaced with the phrase "my plants" while retaining the meaning.