Firstorder equivalence and DeMorgan’s laws
Firstorder equivalence describes a situation in which two sentences are logically
equivalent by virtue of the truthfunctional 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 firstorder equivalent, then they share the same truth conditions and will
always have the same truth value.
A deeper discussion of firstorder eqivalence must begin with a review of DeMorgan’s
laws for truthfunctional 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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 Fall '06
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 Logic, connectives

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