Anyone who has worked with programming knows that boolean logic is hard to express in english. Given the statement "A and B must be false", with no context one can understand the statement to mean

  • A must be true and B must be false
  • The value of A and B must be false (Thus, A,B or A and B must be false)

This ambiguity in English is the source of lots of software bugs -- De Morgan's law is easy to remember but hard to apply when your native language doesn't require it, as are several other logical identities.

I was curious to know, are there any natural or constructed spoken languages (Not languages constructed for explicitly expressing boolean logic) where Boolean logic can be expressed without ambiguity?

  • 1
    No. Nor do I agree that ambiguity is any special problem for programmers.
    – Greg Lee
    May 7 '18 at 9:28

Let's say that by "Boolean logic" you mean "Formal logic", and, moreover, let's restrict your question to the example you are commenting about, rather than to the whole logic.

A first, obvious, answer is no, since, by definition, no natural language is a formal language, and ambiguity is always to be taken into account.

However, your question can be reformulated in a more linguistic fashion: is there any language distinguishing nominal conjunction from predicate conjunction? If attested, such a system could potentially express the difference between

P(a & b)


P(a) & P(b)

Now, such languages are effectively known to exist. Here you can see a map showing the world-wide distribution of languages where the two conjunctions coincide and of those where they do not: http://wals.info/feature/64A#2/25.5/149.0

Famously, many of the oldest Indo-European languages did distinguish two types of conjunction. Thus, in Latin we have the conjunction et and the clitic conjunction -que (often repeated). The former is more general, but is the only one possible with predicates (at least, to my knowledge). The latter is used preferably, perhaps exclusively, with nominals:

genus […] hominum-que ferarum-que et genus aequoreum (Vergil, Georgics, III.242)

‘the race […] of men and of beasts and the race of the see-animals’, possibly to be understood as: ‘(the race of (men & beasts)) & (the race of the see-animals)’

Whether this amounts to a net distinction of P(a & b) from P(a) & P(b), is yet to be proven (and is effectively an interesting topic for an investigation).

Speaking more generally, your question regards the relationship between the logical form of a proposition and the superficial form of a sentence. The logical form of a proposition is an abstract object, while its symbolic representation depends on what symbolism you choose (e.g. think about the difference between "Polish notation" vs. classical notation of the predicates). However, we can empirically claim that no symbolic representation of the logical form coincides with the superficial linguistic form of the sentence. According to Chomsky's theory, there are even explicit grammatical rules translating from the former to the latter. Therefore, languages can differ as to the degree of logical ambiguity they introduce during this translation process.

  • Boolean logic could be taken to mean propositional logic, as opposed to predicate logic.
    – Greg Lee
    May 8 '18 at 1:38

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