Translate the numbered propositions below into GPL. 1. Only logicians prefer Aristotle to Plato. 2. Everyone disagrees with at least one thing that Plato said.
Question
Translate the numbered propositions below into GPL.
- Only logicians prefer Aristotle to Plato.
- Everyone disagrees with at least one thing that Plato said.
Solution
Sure, here are the translations of the propositions into Generalized Propositional Logic (GPL):
-
For the first proposition "Only logicians prefer Aristotle to Plato", we can translate it as follows:
∀x (Prefers(x, Aristotle, Plato) → Logician(x))
This reads as "For all x, if x prefers Aristotle to Plato, then x is a logician."
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For the second proposition "Everyone disagrees with at least one thing that Plato said", we can translate it as follows:
∀x ∃y (Said(Plato, y) ∧ Disagrees(x, y))
This reads as "For all x, there exists a y such that Plato said y and x disagrees with y."
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