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Re: [ontolog-forum] Conjunction and Disjunction

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 03 Jul 2009 15:10:19 -0400
Message-id: <4A4E579B.20407@xxxxxxxxxxx>
Rich,    (01)

I changed the subject line to indicate a switch to a much narrower
discussion that the Semantic Systems thread.    (02)

RC> I see it as two disjuncts:
 >      1.    Paul goes to the water fountain;
 >      2.    Wanda goes to the water fountain;    (03)

Whenever you can paraphrase something with the word 'and', you
have a conjunction.  If you need the word 'or', it's a disjunction.    (04)

In this example, you could paraphrase a list of those two sentences
as "Paul goes to the water function, and Wanda goes to the water fountain."    (05)

There is no implication that they both went together or separately.
In fact, the operator & in FOL obeys the following two inference
rules (using the turnstile operator '|-' to mean 'is provable from'):    (06)

    p, q  |-  p&q    (07)

    p&q  |-  p, q    (08)

RC> I don't think that Paul and Wanda have anything else going...    (09)

Combining two sentences in English or any notation for FOL into
a compound sentence connected by 'and' has no additional
implications beyond what is implied by stating them separately.    (010)

In case of an English narrative, there might be an implicit
'and then' between the sentences.  But the compound sentence
"p, and then q" implies "p and q".    (011)

However, I will admit that the following sentence is ambiguous:    (012)

    Paul and Wanda went to the water fountain.    (013)

This sentence suggests, but does not imply that they went
together.  But in the following context, there is no such
implication:    (014)

    Q: Did anybody in the department go to the water fountain?    (015)

    A: Paul and Wanda did.    (016)

In any case, none of these paraphrases used the word 'or'.    (017)

John    (018)

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