LPL 10.3 lecture

# LPL 10.3 lecture - First-order equivalence and DeMorgans...

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First-order equivalence and DeMorgan’s laws First-order equivalence describes a situation in which two sentences are logically equivalent by virtue of the truth-functional connective, the identity predicate, and quantifiers, or some combination of these. Here, the meanings of the predicates do not need to be known in order to determine that the two sentences are equivalent. If two sentences are first-order equivalent, then they share the same truth conditions and will always have the same truth value. A deeper discussion of first-order eqivalence must begin with a review of DeMorgan’s laws for truth-functional connectives. As we know from earlier chapters, the following pairs of sentences are logically equivalent: ¬ (Cube(a) Tet(b)) ¬ Cube(a) ¬ Tet(b) ¬ (Cube(a) Tet(b)) ¬ Cube(a) ¬ Tet(b) We can also apply DeMorgan’s laws to sentences that contain quantifiers, but in two different ways. The first is to apply DeMorgan’s laws to sentences that are essentially

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LPL 10.3 lecture - First-order equivalence and DeMorgans...

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