Examples
A sentence is either true or false under an interpretation which assigns values to the logical variables. We might for example make the following assignments:
Individual constants
- a: Socrates
- b: Plato
- c: Aristotle
Predicates:
- Fα: α is sleeping
- Gαβ: α hates β
- Hαβγ: α made β hit γ
Sentential variables:
- p "It is raining."
Under this interpretation the sentences discussed above would represent the following English statements:
- p: "It is raining."
- F(a): "Socrates is sleeping."
- H(b,a,c): "Plato made Socrates hit Aristotle."
- x(F(x)): "Everybody is sleeping."
- z(G(a,z)): "Socrates hates somebody."
- xyz(H(x,y,z)): "Somebody made everybody hit somebody."
- xz(F(x)&G(a,z)): Everybody is sleeping and Socrates hates somebody.
- xyz (G(a,z)H(x,y,z)): Either Socrates hates somebody or somebody made everybody hit somebody.
Read more about this topic: Descriptive Interpretation
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