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I have task regarding formalization in first order predicate logic.

The natural language goes:

"Peter Petson is either completely tone-deaf or is listening to Professor Charles. Everyone who listents to Doctor Jeff, also listens to Professor Chales, unless they are totally tone-deaf. We must therefore conclude, that Peter Petson is not listening to Doctor Jeff."

I have tried to formalize it as such:

Constant p = Peter Petson Predicates T(x) = "x is totally/completely tone-deaf" P(x) = X is listening to Professor Charles" D(x) = "x is listening to Doctor Jeff."

And the full formalization: ¬T(t) ∧ ¬P(t) ∀x(D(x) ∧ ¬T(x) → P(x)) ¬D(t)

All help is welcome!

emma
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1 Answers1

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Hint

You have introduced the individual constant $p$ to name Peter Petson; thus, you have to use it to formalize "Peter Petson is either completely tone-deaf or is listening to Professor Charles".

Also Doctor Jeff and Professor Charles needs individual constants: $j$ and $c$.

If so, to formalize "Peter Petson is listening to Professor Charles" we need a binary predicate $P(x,y)$ that means "x is listening to y". In this way, the conclusion will be: $\lnot P(p,j)$

Mauro ALLEGRANZA
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