Is there a logical symbol for 'may include'?
Hi all! I'm working on a personal project, and I find myself looking for a symbol that means something close to 'may include', 'optionally include', or 'inductively suggests'
Phrased in terms of set theory, I'm looking for the _ in
1. Let c ? o
2. Let i ? c
3. Therefore, i _ o
I suspect/hope that there may be something hiding somewhere in the thousands of Unicode symbols but most of them have visual, rather than logical descriptions, and much of the logical descriptions are above my head embedded as I am in my comfortable armchair.
What is striking to me is that there isn't something jumping out immediately, since there seems to be commonly used memberwise set equivalents for all the applicable common numeric predicates, except ?.
Phrased in terms of set theory, I'm looking for the _ in
1. Let c ? o
2. Let i ? c
3. Therefore, i _ o
I suspect/hope that there may be something hiding somewhere in the thousands of Unicode symbols but most of them have visual, rather than logical descriptions, and much of the logical descriptions are above my head embedded as I am in my comfortable armchair.
What is striking to me is that there isn't something jumping out immediately, since there seems to be commonly used memberwise set equivalents for all the applicable common numeric predicates, except ?.
Comments (10)
Set theory may have something like what you are looking for. But logic uses the Aristotelian either/or.
Maybe you could say more about what you are looking for.
I would like to find a relatively unambiguous character in Unicode which some field has used to represent (optional or possible) (inclusion association). A possible example of use:
Sandwich ? Bread
Sandwich ? Cheese
where ? is the symbol I'm trying to find.
I understand your request. Maybe there is something in the Unicode that does that.
But I doubt it, for reasons already offered.
https://en.wikipedia.org/wiki/Modal_logic
Oh that is a good call! That page mentions C.I. Lewis coined a 'possibly', '?', which seems pretty good to me. It's used as a prefix rather than an infix but it's close enough that, unless something much better presents itself, I am going to use that. Thanks so much, both fishfry and Valentinus, for your time and thoughtful responses.
That's right. Not necessarily not ( [math]¬?¬[/math] )
is equivalent to possibly ( [math]?[/math] ) in modal logic
Also, If you want to define the probability that it's an element or a subset, negligible functions could come in useful. It's kind of like a lower bound of likelihood:
https://en.wikipedia.org/wiki/Negligible_function#Examples (not negligible)
If the probability is at least polynomially small i.e noticeable.
A function [math]µ(n)[/math] is noticeable [math]iff[/math]
[math]?c ? N, n0 ? N[/math] such that [math]?n ? n0[/math], [math]µ(n) ?n^{-c}[/math]
[math]?c ? N, n0 ? N[/math] ..
[i]A function [math]µ(n)[/math] is non-negligible (more likely than not) [math]iff[/math]
[math]?c ? N[/math] such that [math]?n0 ? N[/math] , [math]?n ? n0[/math] such that [math]µ(n) ? n^{?c}[/math]
[math]?c ? N[/math] ..
You may use Sandwich ?? (Bread ? Cheese)
Notation: possibly and intersection. You may consider identity and union too, perhaps.
Check this link for notation: https://img1.wsimg.com/blobby/go/c2373a8f-5536-423d-8cc4-fb83be42f049/downloads/Characters-UnicodeDotOrg.pdf?ver=1574920094574
Parent link: https://curp.godaddysites.com/projects
Thanks so much for that suggestion, it's a little over my head and probably out of scope for the kind of conceptual modelling I'm doing, but I'm fascinated by all this stuff and I'm definitely going to add that to my list of conceptual jewellery stores to rob.
Awesome, cheers for that, it's very neat. I'm sure I'll incorporate that in somewhere too.
You're vey welcome Leon. It's a little over all of our heads in my opinion, which is why it's interesting.
It's a good idea for a Philosopher's postgraduate maybe, to investigate the formalism for what negligible means, and if such a definition is justified or not and if not, then why/why not, in what context etc.
1. The choices may include Hitchens' razor
2. If the choices may include Hitchens' razor then the panel may include an Imam
Ergo,
3. The panel may include and Imam
As far as I can tell, the phrase "may include" has no logical significance, at least in the argument as I crafted it above.