LPL 9.5 lecture

LPL 9.5 lecture - Simple translations with quantifiers...

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Simple translations with quantifiers Early work with quantifiers can be found in Aristotle. Aristotle identified four basic types of quantified sentences, which we can represent with the following four English expressions: All P’s are Q’s Some P’s are Q’s No P’s are Q’s Some P’s are not Q’s Studying Aristotle’s forms will help us learn to translate between natural language and FOL. Consider the first two of the forms. The form All P’s are Q’s is translated as: x (P(x) Q(x)) All cubes are small. x (Cube(x) Small(x)) Every cube is small. x (Cube(x) Small(x)) If there is a cube, then it is small. x (Cube(x) Small(x)) Notice that for this type of sentence, the FOL translation will consist of a universal quantifier that scopes over a conditional statement. The form Some P’s are Q’s is translated as: x (P(x) Q(x)) Some cubes are small. x (Cube(x) Small(x)) At least one cube is small. x (Cube(x) Small(x)) There is a small cube. x (Cube(x)
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LPL 9.5 lecture - Simple translations with quantifiers...

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