What does "one-point rule using Z" mean?
In both of your postings, the logical symbols appear to be out of main stream logical notation.
Perhaps you should post a guide to their meaning.
Hello guys!
First of all i would like to express my happiness of the forum coming back live. Nothing is better than this .
I'm not quite sure if anyone here has used Z to represent discrete mathematics here before. But this is the notation which i've been taught at the uni. But since i'm not having much of a help on this. I'm a bit feeling a bit left alone. I got to finish this assignment off I about week time.
Could anyone please help me point out some direction on where to start? Which inference rule to apply first to simplify the following quantification using one-point rule and predicate logic
'z' is assumed to be an integer.
As you can see in the predicate part the implication holds. But i'm quite struggling to understand what is actually represnting. 'z' can be an positive or a negative integer. If y is not equal to z meaning that y is always above 0 as its of type natual number.
thanks a lot guys
ssharish
Thanks for the reply Plato, I completely agree on why this notation seems to be quite unclearly. I rather have been in an understanding that the notation which I’m using is rather nonstandard. But quite not sure as to why my professor seem to use rather a nonstandard notation to represent the quantification and other discrete logic equation. We study formal methods in which we use Z notation.
The link below is the book which I’m referring to and also why professor uses it for his teaching. I don’t expect you to go through all the whole book. But that’s there for your reference.
http://www.cs.cmu.edu/~15819/zedbook.pdf
Out of curiosity, what is a standard notation. Is there a material which i can go through. I'm sorry this might be a simple question. Forgive my silliness.
One point rule is one of the inference rule which actually states as follow
If
the identity of a bound variable is revealed within the quanti
ed expression,
then we may replace all instances of that variable, and remove the existential
quanti
er. Consider the following predicate:
This states that there is a value of x in a for which p ^x ƒt is true. If t is in a,
and p holds with t substituted for x, then t is a good candidate for this value.
Refer page 48 from the above link.
thanks
ssharish
this appears to be a logic problem, though, not a computer science problem. i could be wrong (i haven't looked at the referenced text in detail) but here : (the colon) is used instead of "is an element of", and the dot just means "such that" or "it is the case that".
Hi all, yes Deveno this is definitely a logic question. But i cant get my head around as to what the quantifier suppose to mean. If i try interpret that into English, could anyone please validate if at all it makes any sense or its just me who not thinking it right. So basically it says
"there exists a x in Natural numbers such that for all y in natural number such that y is not equal to z or y is not equal to x implies for all y in natural numbers such that z is greater than y
z is assumed to be an integer "
What I don’t understand is the predicate y not equal to z or y not equal to x. This just doesn’t make sense. z here can have value of both positive and negative in range. Does this mean that y is proving that it will always be positive? If that was the case, we have already proved that because y is of type natural number which means that it can’t hold a value bellow 0!
thanks
ssharish
What exactly do you want to do with this expression: prove it? It is true when z is a natural number because then for x = z both the premise and the conclusion are false. However, when z is negative, it is false because the conclusion is still false, but the premise is true: every natural number y is different from z.
I am not sure if Z considers a well-formed formula when and . But if it does, then I think its meaning is obvious: y and z have the same numerical value.