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LPL 3.5-3.6 lecture - Ambiguity and parentheses Unlike FOL...

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Ambiguity and parentheses Unlike FOL, many English language sentences can be ambiguous. Consider the following sentence: Max is home or Claire is home and Carl is happy. Home(max) Home(claire) Happy(carl) This complex sentence is ambiguous in two ways. It can either be interpreted as a conjunction between the first two atomic sentences and the last, or as a disjunction between the first atomic sentence and the last two. So, in FOL, two different translations are possible for this sentence. (Home(max) Home(claire)) Happy(carl) Home(max) (Home(claire) Happy(carl)) Notice that in FOL, parentheses are used to avoid the ambiguity of multiple interpretations for a single sentence. Parentheses are also necessary in determining the scope of any negation symbol that appears in a complex sentence. ¬ Home(claire) Home(max) ¬ (Home(claire) Home(max)) The first sentence is a conjunction of two literals while the second sentence is a negation.
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