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A First order logic : Predicates

  1. Jun 1, 2017 #1
    I have a small problem with the first order logic, in particular, predicate logic

    Let us take this sentence as an example:

    Each teacher has given a form to each student.

    From this sentence, can we have different reading?

    This is my try to solve such problem, I did not know if this is the answer for such question:

    Every Teacher has given a form to each Student.

    (∀x)Teacher(x)^(∀y) Student(y)^(∃z)Form(z)^Give(x,y,z)

    If X is a Student then he has received a form from a teacher

    Student(x)→(∃y) Teacher(y)^(∃z)Form(z)^Give(x,y,z)

    If X is a Teacher then he has gave a from for all his students

    Teacher(x)→(∀y) Student(y)^(∃z)Form(z)^Give(x,y,z)

    If X is a form then a teacher gave it to all student.

    Form(x)→(∀y) Employer(y)^(∃z)Teacher(z)^Give(x,y,z)
  2. jcsd
  3. Jun 1, 2017 #2


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    There are really only two reasonable interpretations of the natural language sentence:

    (1) Every teacher has given a form to every student, so that if there are N teachers then every student has received N forms


    (2) Every student has received a form from a different teacher. For this to work, the number of teachers must be the same as the number of students.

    I think (1) sounds more plausible.
    This says: everybody is a teacher and everybody is also a student and there is a single form that every person has given to every other person. That doesn't match either of the possible interpretations.
  4. Jun 1, 2017 #3
    Thanks for your reply.

    I think that the form is in logical dependency, either of student, either of teacher, or both, so we can find three other readings, right?

    And How can I transform this sentence then?

    Each teacher has given a form to each student.
    Last edited: Jun 1, 2017
  5. Jun 4, 2017 #4


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    This is more a rule of thumb than an actual full answer. Try different (Logical) worlds/universes, different predicates and see if you get what you would expect to get. Then tinkering may hopefully lead you to the right set up.
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