Re: Representation of "slightly greater than"

Its WYSIWYG in logic:
What you say is what you get.

You could also define:

d(p,q): function that computes distance between p and q
Ex.: if p and q are points in space, i.e. p=<x1,y1>
and q=<x2,y2>, you could use:
d(p,q):= sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))

c(d): function that classifies distance as {close, near, far}
Ex.: if close means around the block, near the same city,
then you could use:
c(d):= close if d<10
near if 10<=d and d<100
far if 100<=d

Then define:
s(p,q): slightly away from me
s(p,q) := c(d(p,q))==close.


The above definition is translation invariant, because
d is already translation invariant. That is:

s(p,q) == s(p+m,q+m)

But you could also define predicates and functions that
have more dependencies.

Bye

s.j.lagoe@xxxxxxxxxxxxxx wrote:
Jan Burse wrote:

You could use fuzzy logic. Then
a statement x<y could have the
valuation 1, 0, 0.7, 0.3, etc..


Thanks for response. Fuzzy logic will definitely help in future
definitions. However currently for "slightly greater than" I thought to
use something like:

[a > b] & ¬[a >> b]

Does this make any sense?



s.j.lagoe@xxxxxxxxxxxxxx wrote:


Hi, I have question related to predicate logic work I do, and wonder if
anyone here might advise. I need to specify quantative amounts, such as
"much greater than" and "few more than". For example, I can write:

Ex A(x) > B(x)

and for much greater than, I can use mathematical symbol >>:

Ex A(x) >> B(x)

However, I want to specify "slightly greater than" and can find no
appropriate denotation. Does anyone know how "a bit more then" can be
formed as a logic statement?

Many thanks for any assistance anyone can help with this very small but
annoying topic.



.