Translate the following natural language statement into a first-order logic

Question

expression in Artificial Intelligence
1. All Students are smart
2. All dogs are mammals
3. Some mammals are not dogs
4. Everyone loves someone
5. Chala bought something

Answer 1

Here are the translations of the given natural language statements into first-order logic expressions:

1. All Students are smart.
   \[ \forall x , (Student(x) \rightarrow Smart(x)) \]

2. All dogs are mammals.
   \[ \forall x , (Dog(x) \rightarrow Mammal(x)) \]

3. Some mammals are not dogs.
   \[ \exists x , (Mammal(x) \land \neg Dog(x)) \]

4. Everyone loves someone.
   \[ \forall x , \exists y , Loves(x, y) \]

5. Chala bought something.
   \[ \exists x , Bought(Chala, x) \]

Each expression uses the following conventions:

• \( \forall \) denotes "for all"
• \( \exists \) denotes "there exists"
• Predicates (like \( Student(x) \), \( Smart(x) \), etc.) represent properties or relations relevant to the objects and individuals in the domain.