Is there a logical symbol for 'may include'?

Leon Spencer

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 ≅.

View Answer

Valentinus

↪Leon Spencer

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.

Leon Spencer

↪Valentinus

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.

Valentinus

↪Leon Spencer

I understand your request. Maybe there is something in the Unicode that does that.
But I doubt it, for reasons already offered.

fishfry

Maybe modal logic can offer some clues. For example there's a "necessarily true" operator, so the negation of that might be what you want.

https://en.wikipedia.org/wiki/Modal_logic

Leon Spencer

↪fishfry

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.

Paul S

For example there's a "necessarily true" operator, so the negation of that might be what you want. — fishfry

That's right. Not necessarily not ( $¬□¬$ )
is equivalent to possibly ( $◇$ ) 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 $µ(n)$ is noticeable $iff$

$∃c ∈ N, n0 ∈ N$ such that $∀n ≥ n0$ , $µ(n) ≥n^{-c}$
$∃c ⊆ N, n0 ⊆ N$ ..

A function $µ(n)$ is non-negligible (more likely than not) $iff$

$∃c ∈ N$ such that $∀n0 ∈ N$ , $∃n ≥ n0$ such that $µ(n) ≥ n^{−c}$
$∃c ⊆ N$ ..

DrOlsnesLea

↪Leon Spencer

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

Leon Spencer

↪Paul S

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.

↪DrOlsnesLea

Awesome, cheers for that, it's very neat. I'm sure I'll incorporate that in somewhere too.

Paul S

it's a little over my head — Leon Spencer

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.

TheMadFool

↪Leon Spencer

While I think @fishfry's answer is the best I wonder whether "may include" has an independent logical meaning that would require separate consideration. Look at the argument below:

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.

Is there a logical symbol for 'may include'?

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