smu-cse-7320

Artificial Intelligence

First-order logic

See puzzles in first-order-logic

puzzle-1

Consider the following puzzle:

1. All who neither dance on tight ropes nor eat penny-buns are old.
2. Pigs, that are liable to giddiness, are treated with respect.
3. A wise balloonist takes an umbrella with him.
4. No one ought to lunch in public who looks ridiculous and eats penny-buns.
5. Young creatures, who go up in balloons, are liable to giddiness.
6. Fat creatures, who look ridiculous, may lunch in public, provided that they do not dance on tight ropes.
7. No wise creatures dance on tight ropes, if liable to giddiness.
8. A pig looks ridiculous carrying an umbrella.
9. All who do not dance on tight ropes and who are treated with respect are fat.

Prove that:

• No wise young pigs go up in balloons.

puzzle-2

Consider the following puzzle:

1. Wolves, foxes, birds, caterpillars, and snails are animals, and there are some of each of them.
2. Also, there are some grains, and grains are plants.
3. Every animal either likes to eat all plants or all animals much smaller than itself that like to eat some plants.
4. Caterpillars and snails are much smaller than birds, which are much smaller than foxes, which in turn are much smaller than wolves.
5. Wolves do not like to eat foxes or grains, while birds like to eat caterpillars but not snails.
6. Caterpillars and snails like to eat some plants.

Prove that:

• There is an animal that likes to eat a grain-eating animal.

Software

Prover9 is an automated theorem prover for first-order and equational logic.

See note for known issues.