LPL 3.5-3.7 lecture

LPL 3.5-3.7 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) [not a sentence of FOL] The English sentence can be read in two distinct ways. It can be interpreted either 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, two different FOL 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 problem of multiple interpretations for a single sentence. Parentheses are also used to mark the scope of negation symbols that modify more than one atomic 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. When are parentheses necessary? P Q R P Q R P Q R In our system, parentheses are necessary only when an ambiguity would result without them. Unnecessary parentheses can be used in order to make a complex sentence more easily readable, while not changing the meaning of the sentence.
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This note was uploaded on 02/10/2011 for the course PHIL 110 taught by Professor ? during the Spring '06 term at South Carolina.

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LPL 3.5-3.7 lecture - Ambiguity and parentheses Unlike FOL...

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