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The question Precedence of “and” and “or” asks if there is any notion of precedence ordering in the English and it would seem not, based on the answers.
Regardless of that, if you saw the following piece of text, how would interpret it and why?
The prerequisite(s) of module AB1234:
GN3001 and GN3002 or BC3006 and BC3007.
I would intepret it as
either "GN3001 and GN3002"
or "BC3006 and BC3007"
are required
But I would also consider that it is badly formulated, and they should have made it crystal clear.
One reason for interpreting this in this way is that the two pair would appear to go together - two GN units or two BC units makes sense ( without knowing what they are ). So there are subtle suggestions in the content that would point me one way or the other.
However, when this is being defined as course pre-requisites, it should be made completely clear and unambiguous. I would feel a need to contact whoever to clarify this, which means that the communication has failed.
We read and interpret one word at a time so, when sentences are ambiguous, we tend to take the narrowest left-hand interpretation. That's why we find garden path sentences (e.g. “Fat people eat accumulates.” or “I convinced her children are noisy.”) so confusing.
In the case of your sentence, when we reach this point:
The prerequisite(s) of module AB1234:
GN3001 and GN3002 …
it looks like GN3001 and GN3002 forms a group so, until we see evidence to the contrary, we keep going with that interpretation. This means that, on first glance, most people would interpret the sentence as meaning:
(GN3001 and GN4003) or (BC3006 and BC3007)
rather than:
GN3001 and (GN4003 or BC3006) and BC3007
((GN3001 and GN4003) or BC3006) and BC3007) OR AA1001 and (BB2002 or (CC3003 and DD4004)) if we're going from left to right?
Feb 20, 2012 at 23:38
Being a fairly pedantic person, I would interpret it only as being highly ambiguous, and I would ask the author for clarification.
The natural way to read it is as SchroedingersCat already mentioned. But this does also works if the pairs were mixed:
(GN3001 and BC3006) or (GN3002 and BC3007)
It has nothing to do with similar IDs for units, it's just a question of how the man's brains works. It isn't important what the numbers are, another example
AA1001 and BB2002 or CC3003 and DD4004
is also read like the first example above:
(AA1001 and BB2002) or (CC3003 and DD4004)
This construction is the simplest way how to structure them and thus this is the way our brain/mind works.
Think of the alternatives:
Even with parenthesis it's not that easy to read. The first alternative interpretation is unlikely, because it does absolutely not fit our brain's/mind's structure. If you wanted to intend that one you ever have to clarify it.
The latter would only concur with our mind structure if you know that the value, performance, ... of BB2002 is greater than or equal to CC3003 and DD4004 together. Though, it is only secondary in our mind, because the logic behind it is also much more complicated.
Thus, in a nutshell, you first connect the both "and"-condition and then choose either of them as the "or"-condition requires.
There is some sense in saying that the precedence of "and" is greater than that of "or". Any given proposition is either true or false (or weird, like "This statement is false," but we'll ignore those here). From a proposition you can obtain more complex propositions using various logical operations, such as "and", "or", and "not". For a more complex proposition built out of simpler propositions and logical operations, you can figure out for any set of truth values for the simpler propositions whether the more complex proposition is true or false. You can represent all truth values of all of the simple propositions and of the more complex proposition using a truth table. If you use 0 to represent false and all other numbers to represent true, multiplication is the same operation as "and" and addition is the same as "or". The standard order of operations gives multiplication higher precedence than addition, which would translate into "and" having higher precedence than "or". However, this is only by convention and thus there is strictly no "from first principles" reason to say that "and" has higher precedence than "or".
ands?