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tl;dr: No. From an engineering perspective, you might be asking if a concatenation operator can be used in place of a logical ‘and’ operator. This is obviously specific to a particular language, bu...
Answer
#2: Post edited
by
r~~
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2020-09-14T21:00:23Z (over 4 years ago)
- tl;dr: **No.**
- From an engineering perspective, you might be asking if a concatenation operator can be used in place of a logical ‘and’ operator. This is obviously specific to a particular language, but I'm not aware of any language in which this is the case, and I've seen a few languages. For most languages with static types, using a concatenator when a logic operator is expected won't even type check; for the others, concat often ends up working more like an ‘or’ than an ‘and’, as detailed in 8063's answer.
From a mathematical perspective, you might be asking if the concept of logical ‘and’ generalizes in any interesting ways such that it might include concatenation under some conditions. ‘Interesting’ here is somewhat subjective, so I can't say absolutely not, but I will say that the typical perspective that a mathematician would take on the generalization of logical ‘and’ and ‘or’ is that they are the two operations of a [lattice](https://en.wikipedia.org/wiki/Lattice_(order)), specifically a [Boolean lattice](https://en.wikipedia.org/wiki/Boolean_algebra_(structure)) (a.k.a. a Boolean algebra). One of the requirements for lattice operations is that they must be *commutative*—that is, the order of their arguments mustn't matter. Another is that they must be *idempotent*—that is, any value combined with itself via the operation must be unchanged. Concatenation violates both of these in general. One can conceive of a generalization of a lattice (or semilattice, if you only care about ‘and’ and not ‘or’) that doesn't carry these restriction, but you'd be giving up very much of what it means to be a lattice in that case, and consequently very very much of what it means to be the logical ‘and’.
- tl;dr: **No.**
- From an engineering perspective, you might be asking if a concatenation operator can be used in place of a logical ‘and’ operator. This is obviously specific to a particular language, but I'm not aware of any language in which this is the case, and I've seen a few languages. For most languages with static types, using a concatenator when a logic operator is expected won't even type check; for the others, concat often ends up working more like an ‘or’ than an ‘and’, as detailed in 8063's answer.
- From a mathematical perspective, you might be asking if the concept of logical ‘and’ generalizes in any interesting ways such that it might include concatenation under some conditions. ‘Interesting’ here is somewhat subjective, so I can't say absolutely not, but I will say that the typical perspective that a mathematician would take on the generalization of logical ‘and’ and ‘or’ is that they are the two operations of a [lattice](https://en.wikipedia.org/wiki/Lattice_(order)), specifically a [Boolean lattice](https://en.wikipedia.org/wiki/Boolean_algebra_(structure)) (a.k.a. a Boolean algebra). One of the requirements for lattice operations is that they must be *commutative*—that is, the order of their arguments mustn't matter. Another is that they must be *idempotent*—that is, any value combined with itself via the operation must be unchanged. Concatenation violates both of these in general. One can conceive of a generalization of a lattice (or semilattice, if you only care about ‘and’ and not ‘or’) that doesn't carry these restrictions, but one would be giving up very much of what it means to be a lattice in that case, and consequently very very much of what it means to be the logical ‘and’.
#1: Initial revision
by
r~~
·
2020-09-14T20:14:08Z (over 4 years ago)
tl;dr: **No.** From an engineering perspective, you might be asking if a concatenation operator can be used in place of a logical ‘and’ operator. This is obviously specific to a particular language, but I'm not aware of any language in which this is the case, and I've seen a few languages. For most languages with static types, using a concatenator when a logic operator is expected won't even type check; for the others, concat often ends up working more like an ‘or’ than an ‘and’, as detailed in 8063's answer. From a mathematical perspective, you might be asking if the concept of logical ‘and’ generalizes in any interesting ways such that it might include concatenation under some conditions. ‘Interesting’ here is somewhat subjective, so I can't say absolutely not, but I will say that the typical perspective that a mathematician would take on the generalization of logical ‘and’ and ‘or’ is that they are the two operations of a [lattice](https://en.wikipedia.org/wiki/Lattice_(order)), specifically a [Boolean lattice](https://en.wikipedia.org/wiki/Boolean_algebra_(structure)) (a.k.a. a Boolean algebra). One of the requirements for lattice operations is that they must be *commutative*—that is, the order of their arguments mustn't matter. Another is that they must be *idempotent*—that is, any value combined with itself via the operation must be unchanged. Concatenation violates both of these in general. One can conceive of a generalization of a lattice (or semilattice, if you only care about ‘and’ and not ‘or’) that doesn't carry these restriction, but you'd be giving up very much of what it means to be a lattice in that case, and consequently very very much of what it means to be the logical ‘and’.