June 1st, 2017, 04:32 AM  #1  
Newbie Joined: Jun 2017 From: Paris Posts: 1 Thanks: 0  First order logic
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 whether this is the answer for such question: Quote:
Last edited by skipjack; June 1st, 2017 at 08:28 AM.  
January 18th, 2018, 08:34 AM  #2  
Newbie Joined: Jan 2018 From: somewhere Posts: 14 Thanks: 2 Math Focus: Algebraic Number Theory / Differential Fork Theory  Quote:
There exists a teacher such that there exists a form such that they gave the form to student x it should be written as: $\exists_{y \in T} (\exists_{z \in F} (Give(x,y,z)))$, where $T$ is the set of all teachers and $F$ is the set of all forms. Note: T and F can be taken from predefined terms. I'm just using that portion to clarify my meaning. This is because $\exists$ and $\forall$ are aggregate operators similar to the summation operator or large product operator. If you don't give it a statement, then it isn't valid notation. This is how I learned it, but it looks better in my opinion. Another way to write it would be to say this. $(y \in T) \land (z \in F) \land (Give(x,y,z))$ It merely states that $y$ is in the set and $z$ is in the set. However, this is mildly flawed as $y$ and $z$ haven't been created yet! So definitely go with the first one assuming $y$ and $z$ are not predefined things that may or may not be forms or teachers and you wish to say are the form and teacher mentioned there.  

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