Slide 1 First-order Logic
Slide 1 First-order Logic
Slide 1 First-order Logic
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Kabos: Intro<strong>Logic</strong> slides 25 Oct 2007<br />
✬<br />
✩<br />
<strong>Slide</strong> 4<br />
U: all animals<br />
A(x): x is an alligator<br />
R(x): x is a reptile<br />
Z(x): x lives at the Zoo.<br />
Some reptile lives at the zoo.<br />
∃x (R(x) & Z(x))<br />
✫<br />
✬<br />
✪<br />
✩<br />
<strong>Slide</strong> 5<br />
U: all animals<br />
A(x): x is an alligator<br />
R(x): x is a reptile<br />
Z(x): x lives at the Zoo.<br />
Every alligator is a reptile.<br />
∀x (A(x) → R(x))<br />
✫<br />
✬<br />
✪<br />
✩<br />
<strong>Slide</strong> 6<br />
U: all animals<br />
A(x): x is an alligator<br />
R(x): x is a reptile<br />
Z(x): x lives at the Zoo.<br />
There are reptiles which are<br />
not alligators.<br />
∃x (R(x) & ¬A(x)) ⇐⇒ ¬(∀x (R(x) → A(x)))<br />
✫<br />
✪
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