Is it a very bad idea to write xor in an article? In writing a paper or thesis, is it a sign of bad style to use xor in your text as a word having the logical meaning of exclusive or? Or should you always avoid:

.. xor ..

by writing something like:

either .. or ..

 A: You are writing an article in English. Therefore, sentences should only contain correct English words, and not some combination of terms you would use in formulas and normal English words. Therefore, I would strongly recommend to use 

either ... or ...

Also, if you are using XOR, you should write it in all-caps  (Sources: Oxford Dictionary, Merriam-Webster) which makes it less attractive to read it in most sentences.
A: It also depends on the topic you write thesis upon. Including logical operations like XOR or maybe some tedious mathematical notations in a thesis on biology or medical sciences  might put the targeted audience in a fix at times. Therefore avoiding these terms and replacing them with simple English might make it convenient for wider audience.
A: My personal preference is to read English words in complete sentences rather than logical reasoning written out in formula-like style. I always have to translate the latter into the former.
I feel the same way about
$$
\sum_{n=1}^\infty f(n)
$$
which I always rewrite as
$$
f(1) + f(2) + \cdots ,
$$
so I can see how the terms change.
A: Either you are writing a formula, in which case xor as an operator might be acceptable (but consider \otimes or some such if speaking in a mathematical framework) OR you are writing text, in which case you should use a textual form, which xor is not. The string xor might be used informally to refer to exclusive-or, but not in formal writing.
Both of these cases cannot be true; they are exclusive.
Note particularly that if you are writing a thesis or article, then you have two goals. One is to communicate as clearly as possible. Another goal is to demonstrate that you can write well and use the language well. It isn't necessarily clear that using xor instead of more traditional forms is more or less clear (it will certainly be less clear for some readers), but it is absolutely certain that using a non-standard word like xor will do yourself a serious disservice with at least somebody you want to impress.
Don't kid yourself by pretending that a thesis is entirely about communication of some novel and great idea. It is also about selling your idea as widely as possible and possibly about selling yourself as well. Anybody who decides that you are an illiterate boob who prefers jargon to clear language is much less likely to take your ideas seriously. As you can see from the comments here, there are at least some people who think that using xor is incorrect usage in text. Did you really want to have those people take your ideas less seriously?
A: (I don't know why this has a downvote, but I sure you it is correct.)
Yes, it's a very bad idea - but not just because it reads awkwardly. From a strictly logical standpoint, xor is really just the wrong tool. For example, consider the...

Trichotomy Axiom (Plain English). If $x$ and $y$ are real numbers, then precisely one of the following holds. $$x<y, \quad x=y, \quad x>y$$

As it turns out, the following statement, while true, actually fails to correctly formalize the above axiom.

Incorrect Formalization (Symbolic). If $x$ and $y$ are real numbers, then: $$(x<y)+(x=y)+(x>y).$$
(Where $+$ means xor).

The correct formalization is:

Trichotomy Axiom (Symbolic). If $x$ and $y$ are real numbers, then: $$[x<y]+[x=y]+[x>y]=1$$
(Where $[\Box]$ is the Iverson bracket and $+$ means the usual notion of addition on $\mathbb{N}$.)

To see the problem with with incorrect formalization, observe that for all booleans $A$,$B$ and $C$, we have:
$$A+B+C \iff [A]+[B]+[C] \in \{1,3\}$$
This can be checked by looking at 4 cases:


*

*$A,B,C$ all false.

*$A,B$ false, $C$ true

*$A$ false, $B,C$ true

*all true


What this tells us is that the Plain English meaning of the incorrect formalization is:

Incorrect Formalization (Plain English). If $x$ and $y$ are real numbers, then either one or all three of the following are true: $$x<y, \quad x=y, \quad x>y$$

But of course, this doesn't agree with the Trichotomy axiom we started with, which in turn proves that the incorrect symbolic formalization is indeed exactly that - incorrect.
