# Translation of English sentences into Logic

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Hi,

I am reading a tutorial which translates the following sentence into logic:

Quote

On sunny days weddings are held in the garden

The translation is:

Sunny_days => garden_weddings

The "implies" formula is given by:

P => Q is given by: ~P V Q

I can't understand this translation. According to the formula we should have:

not sunny_days V garden_wedding

which can be stated in English as:

On sunny days weddings are held in the garden However the tutorial translates it into:

"Either not sunny days weddings are held in the garden"

I can't understand this, why we have 'not" before sunny_days. Original sentence does not use 'not' with sunny_days. I have attached the tutorial file. Somebody please guide me.

Zulfi.

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6 hours ago, zak100 said:

P => Q is given by: ~P V Q

I can't understand this translation.

It is explained in detail in the document, especially the part where the truth table for both expressions are compared:

Quote

It is possible to substitute one equivalent expression for another without changing the meaning of what is being represented, since the “meaning” of a propositional expression is fully defined by its truth table. For example consider the following statement:

“On sunny days weddings are held in the garden.”

This statement could be roughly approximated by the propositional expression:

(1) sunny_day ⇒ garden_wedding

From the equivalences given in Figure 14.33, we know that this expression could be replaced with the following:

(2) ~ sunny_day  garden_wedding

These two expressions, (1) and (2), are “logically equivalent”, but does the result of the substitution still make sense to a human? With some thought we can see that the answer to this question is “yes”. The new form of the statement, (2), would roughly translate back into English as:

“Either it is not a sunny day or weddings will be held in the garden”.

Upon reflection, you should be able to see that statements (1) and (2) are expressing the same idea. When one is true, the other is true. When one is false, so is the other. If you have trouble seeing this, look back at the truth tables for P ⇒ Q and ~ P  Q in part (b) of Figure 14.33 and think carefully about the circumstances represented by each row.

Maybe you could give some more detail about with step that causes trouble.

6 hours ago, zak100 said:

I can't understand this, why we have 'not" before sunny_days.

Without the "not" we have the expression  "sunny_day ∨ garden_wedding" instead of the tutorial's "~ sunny_day ∨ garden_wedding"
That implies that there could be sunny days with weddings not in the garden and that is not what the original sentence says. Expression "sunny_day ∨ garden_wedding" is more like "On sunny days weddings are sometimes held in the garden and sometimes not.”

Edited by Ghideon
clarified

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simply, I see the use of "de morgan" rules.

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Hi,

"On sunny days weddings are sometimes held in the garden and sometimes not.”

The above is a good answer.

God blesses you.

If there is problem I would state again.

Zulfi.

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f

11 minutes ago, zak100 said:

"On sunny days weddings are sometimes held in the garden and sometimes not.”

The above is a good answer.

Thanks. Please not though that specific the sentences you quote was an example of an invalid answer. I posted that to highlight what happens when the negation is dropped per your  request; without negation it allows for weddings to be held at other places (for instance indoors) even if it is a sunny day. Maybe I should have posted a more explicit sentence:

Incorrect, no negation: "sunny_day ∨ garden_wedding" = "On sunny days weddings are sometimes held in the garden and sometimes not held in the garden, for instance indoors.”

Correct, as per tutorial, with negation:  "~ sunny_day ∨ garden_wedding" = “On sunny days weddings are held in the garden.”

The tutorial's sentence disallows indoor weddings on sunny days but does not disallow garden weddings on a rainy day. The incorrect sentence (no negation) incorrectly allows indoors weddings on sunny days.

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10 hours ago, zak100 said:

"On sunny days weddings are held in the garden"

The translation is:

Sunny_days => garden_weddings

The original statement has multiple interpretations, left ambiguous by your translation. This being a topic concerning translation of English to logic, I approve the translation.

The two interpretations seem to generate mutually exclusive statements.  Each has implications seemingly opposite of each other. The interpretations break into logical statements involving two of three variables: S(sunny), G, and E for weddings in garden and elsewhere respectively. Note that neither interpretation is a function of all three variables.  Both G and E can be false if no weddings are held that day, and can both be true if weddings are held in both places.

Interpretation 1:

On sunny days, all weddings are held in the garden.   S => ~E

This implies that if there is an indoor wedding, it is not a sunny day.  It does not imply that if it is a sunny day, there is a wedding.

Interpretation 2:

On sunny days, there are weddings held in the garden.    S => G

This implies that if there are no weddings today, it is not a sunny day.  It does not imply that if there is an indoor wedding, it is not a sunny day.

Edited by Halc

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Hi,

Thanks. If I get time, I would come back to your post.

God blesses you for giving me more explanation. Surely this would help others.

Zulfi.

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On 10/25/2020 at 4:03 AM, zak100 said:

On sunny days weddings are held in the garden

That sentence is ambiguous.

Do they mean "if it's raining, they are held in the church"

Or does it mean "if it's raining, they are not held"

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10 hours ago, John Cuthber said:

That sentence is ambiguous.

Do they mean "if it's raining, they are held in the church"

Or does it mean "if it's raining, they are not held"

True.

I this case though the tutorial OP refers to they have decided on one meaning and then they use that as an example:

Quote

For example consider the following statement:


“On sunny days weddings are held in the garden.”


This statement could be roughly approximated by the propositional expression:

(1) sunny_day  garden_wedding

(From the document attached to first post)

Side note: I find John's comment interesting in relation to use of machine translation and intent extraction. I did not think the sentence was very ambiguous when reading the tutorial, but that was probably because I was biased by the choice already made by the author. Also, english is not my first language and the level of ambiguity may not be the same when translating back and forth. I have no source to support this observation, it's mote a personal note.

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1 hour ago, Ghideon said:

(1) sunny_day  garden_wedding

Odd.

What if there are no couples wishing to get married that week?

What if it's sunny, but also very cold?

It is currently sunny in my garden but I don't see any weddings.

Translating human language is difficult- partly because people are enormously clever and can cope with this level of ambiguity.

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Much as I hate to agree with John Cuthber, I have to in this case.

The original statement is a very poor example that IMHO cannot be translated into formal logic.

It is meaningless without the context that would remove the ambiguities John mentioned.

English permits many forms of statement that are excluded from formal logic.

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24 minutes ago, John Cuthber said:

Odd.

3 minutes ago, studiot said:

It is meaningless without the context that would remove the ambiguities John mentioned.

I agree to both.

I have not researched the source in any extent, there may be more context given by the author. But I would not be surprised if the linked document deliberately used a vague english statement with the intention to inspire comments like those from John and studiot.

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29 minutes ago, Ghideon said:

But I would not be surprised if the linked document deliberately used a vague english statement with the intention to inspire comments like those from John and studiot.

It's not vague. It's actually quite clear and precise.

It's just that you would never come out with a statement like that on its own.

The Germans have an expression for what it is not

Ist noch nicht selbsverstandlich.

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2 hours ago, John Cuthber said:

Odd.

What if there are no couples wishing to get married that week?

What if it's sunny, but also very cold?

It is currently sunny in my garden but I don't see any weddings.

Translating human language is difficult- partly because people are enormously clever and can cope with this level of ambiguity.

mmm ,well.

probably this is being caused by this:

""logic " is a subject or branch of  mathematics, which does not deal with propositions, it tries to prove or make proofs for propositions instead(generally) with global truths and scientific truths. ) "

Edited by ahmet
spelling and punctuational errors

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