How do we represent the above facts in

1)axiom form and
2)clausal form

1) All babies are innocent
2) Anyone who is innocent and affectionate will be loved by others
3) Anyone who is loved by others, will receive gifts
4) Teena is an affectionate baby

My thoughts on the question : (Let Vx and Ex denote universal and existential quantifiers respectively )

Let B(x) denote x is a baby
I(x) denote x is innocent
A(x) denote x is affectionate
L(x) denote x is loved by others
G(x) denote x receives a gift

Axiom Form :
1) Vx[ B(x) --> I(x) ]
2) Vx[ I(x) ^ A(x) ] --> L(x)
3) Vx [ L(x) --> G(x) ]
4) B(Teena) --> A(Teena)

Have I done the first part correctly?

And how do we do the second part?

Thanks!

Yes, you have correctly represented the given facts in axiom form. Each of the four statements has been converted into a logical statement using symbols and quantifiers.

To represent the facts in clausal form, we will convert each logical statement into a set of clauses. A clause is a disjunction of literals (either positive or negated) connected by logical OR.

Clausal Form:
1) {~B(x), I(x)}
2) {~I(x), ~A(x), L(x)}
3) {~L(x), G(x)}
4) {~B(Teena), A(Teena)}

In the clausal form, each statement is split into several clauses based on the logical connectives present in the original statements. The negation of each statement is used to construct the clauses.

In this case, the given statements do not have any negated literals. Therefore, each statement is simply split into individual clauses based on the conjunctions (logical AND) present in the statements.

So, your clausal form representation is as follows:
1) {~B(x)}, {I(x)}
2) {~I(x)}, {~A(x)}, {L(x)}
3) {~L(x)}, {G(x)}
4) {~B(Teena)}, {A(Teena)}

Each clause represents a separate piece of information that can be used by an inference engine or a theorem prover to reason about the facts.

I hope this helps! Let me know if you have any other questions.