Translating to Predicate Logic with Lexicon
The first step is to define the alphabet. Take the following first-order alphabet with the required interpretation:
- S (x): "x is a student"
- E (x): "x is the examiner"
- G (x): "x - class"
- D (x): "x disappointed"
- R (x, y): "x is a requirement for y"
- B (x, y): "x is y or better"
- O (x, y): "x takes y"
- H (x, y, z): "x hopes y satisfies z"
e: Constant ("class E")
x, y, z, w: Variables
Let's break down the original statement in two parts:
S1: "Assessor hopes that all students will meet the requirements for grade E or better"
S2: "Someone gets a lower grade and will be disappointed"
And use a specific alphabet to spell it in first order:
S1: ∃x (E (x) ∧ ∀y (S (y) ⇒ ∃z∃w (R (z, e) ∧ B (w, z) ∧ H (x, y, w))))
S2: ∃x∃y (S (x) ∧ G (y) ∧ O (x, y) ∧ ¬B (y, e) ∧ D (x))
Finally, we'll compute the original statement, that is:
S1 ∧ S2
Keep in mind that this is only one of the interpretations that will lead to the correct (satisfactory) answer.
I hope this helps
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