CODEWITHSUNDEEP
nlplogicpredicate
tavalendo
tavalendo

Reputation: 877

Translation to Predicate Logic with Lexicon

How would one translate the following statement into predicate logic:

"Even though the examiner hopes all students will satisfy the requirements for grade E or better, somebody will receive a lower grade and be disappointed."

Upvotes: 3

Views: 399

Answers (1)

playful
playful

Reputation: 1774

The first step is to define an alphabet. Take the following first-order alphabet with the desired interpretation:

Unary predicates:

  • S(x): "x is a student"
  • E(x): "x is an examiner"
  • G(x): "x is a grade"
  • D(x): "x is disappointed"

Binary predicates:

  • R(x, y): "x is a requirement for y"
  • B(x, y): "x is y or better"
  • O(x, y): "x receives y"

Ternary predicates:

  • H(x, y, z): "x hopes that y fulfills z"

e: Constant ("the grade E")

x, y, z, w: Variables

Let's break the original statement in two parts:

S1: "The examiner hopes all students will satisfy the requirements for grade E or better"

S2: "Somebody will receive a lower grade and be disappointed"

And use the defined alphabet to write 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 compute the original statement, that is:

S1 ∧ S2

Keep in mind that this is just one of the interpretations that will lead to a correct (satisfying) answer.

I hope it helps

Upvotes: 2

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