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A sentence is in Disjunctive Normal Form if it is a disjunction, the disjuncts of which are themselves conjunctions of sentence letters and negated sentence letters. In this characterization we allow as a special case that a disjunction may have only one disjunct and a conjunction may have only one conjunct.

(You don't have to understand this logical jibberish.)

Does may here mean can or might? The difference is significant: it either must have only one disjunct, or it might have one or a different number of disjuncts.

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    It's ambiguous as the syntax allows either, but based on the context I would say can, because it seems to be describing optional properties/relationships. Might is more appropriate for possibility or uncertainty - if there were a conditional clause adjacent, it would be more ambiguous.
    – jimsug
    May 20 '14 at 10:58
  • Broadly, 'can' refer to the capability of someone/thing and on the other hand, may shows possibility of someone/thing. IMO, may fits better. Now, may and might are interchangeable (though prefer may) as the sentence is not in past. And thanks, I din' try to understand the paragraph after your clarification ;)
    – Maulik V
    May 20 '14 at 11:11
  • I didn't read the whole text, but I think replacing that may with might is weird, though replacing it with can is possible. I believe that what the text really wants to say is "a disjunction must have either zero or one disjunct and a conjunction must have either zero or one conjunct." -- My reading might be off because I didn't really read your text. May 20 '14 at 13:59
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What the authors clearly intended this to mean (I can deduce this from my knowledge of the subject being discussed) is that a disjunction is allowed to have one or more disjuncts, and a conjunction is allowed to have one or more conjuncts.

I don't think that's what it actually means. Usually in English, when may means allowed to, the phrase may have only one means may not have two or more.

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  • When taken out of context, it is possible to interpret may have only one as may have at most one. ("You may have only one cookie" = "No more than one cookie for you".) However, in this context, "we allow as a special case" makes it perfectly clear that your first interpretation is the only one that makes sense, because two or more is the "usual" case. May 20 '14 at 15:29
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It means both can and might. Unfortunately, Can, might and may are interchangeable here. There may be slight differences in nuance, but they all mean in this case that something is allowable.

The good news is, from the context it is clear that may have means possibly has:

A disjunction possibly has only one disjunct.
A disjunction is still a disjunction if it has only one disjunct.

Why is the context clear? Because mention is made of a special case. If what followed were to be the rule, it would not constitute a special case!

Also, in case that must were meant, I hope the author would have used that verb, as it avoids confusion as to the necessity of what follows:

A disjunction must have one or more disjuncts.

That line describes the disjunction as a combination of what your text implies:

  • A disjunction has two or more disjuncts.
  • Additionally, it may have only one disjunct.
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A disjunction is an expression of the form a ∨ b, where is the Logical OR operator.

A conjunction is an expression of the form a ∧ b, where is the Logical AND operator.

A sentence is in Disjunctive Normal Form if it is of the form

c1c2c3 ∨ …

where each ci is of the form

d1d2d3 ∧ …

The last sentence

In this characterization we allow as a special case that a disjunction may have only one disjunct and a conjunction may have only one conjunct.

… means that degenerate cases can also be considered sentences in Disjunctive Normal Form. For example, x ∧ y is in DNF even though there is no operator, because "a disjunction may have only one disjunct". Similarly, (x ∧ y) ∨ z is also in DNF, even though z is on its own, because "a conjunction may have only one conjunct". Taken together, the degenerate cases allow you to treat just x as simultaneously a DNF sentence, a conjunction, and a disjunction.

As for the choice of modal verb, may is most appropriate. Can could also work, and in my opinion would be synonymous in this context. Might is less appropriate, but even if it were used, I don't think it would make any difference in meaning either.


Addendum

It turns out that "In this characterization we allow as a special case that…" is key to interpreting the sentence.

In other contexts, "may have only one" could very well mean either

  • has exactly one

    For example, "A unicycle may have only one wheel." That's a bit odd, though, since it would be better to say "A unicycle has one wheel".

  • may have at most one

    For example, "You may have only one cookie." In that case, taking a second cookie would be antisocial.

If "In this characterization we allow as a special case that…" were omitted, then the at-most-one-cookie interpretation would be the most straightforward interpretation. However, since "special case" is mentioned, you first have to consider what is the "usual" case. The usual case is that a conjunction or disjunction has two or more operands. In that frame, the only reasonable interpretation of "may" is that it "gives permission" to include the case where a conjunction or disjunction has just one operand. The framing has much more influence on the meaning of the sentence than the choice of modal verb, and therefore it makes no difference which modal verb is used.

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