Translating Sentences From A Natural Language Into An Artificial Language
Sentences in natural languages can be ambiguous, whereas the languages of the sentential logic and predicate logics are precise. Translation can reveal such ambiguities and express precisely the intended meaning.
For example take the English sentence “Father Ted married Jack and Jill”. Does this mean Jack married Jill? In translating we might make the following assignments: Individual Constants
- a: Father Ted
- b: Jack
- c: Jill
Predicates:
- Mαβγ: α officiated at the marriage of β to γ
Using these assignments the sentence above could be translated as follows:
- M(a, b, c): Father Ted officiated at the marriage of Jack and Jill.
- ∃x ∃y (M(a, b, x) ∧ M(a, c, y)): Father Ted officiated at the marriage of Jack to somebody and Father Ted officiated at the marriage of Jill to somebody.
- ∃x ∃y (M(x, a, b) ∧ M(y, a, c)): Somebody officiated at the marriage of Father Ted to Jack and somebody officiated at the marriage of Father Ted to Jill.
To establish which is the correct translation of “Father Ted married Jack and Jill”, it would be necessary to ask the speaker exactly what was meant.
Read more about this topic: Atomic Sentence
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