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
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
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