Wikipedia:Reference desk/Archives/Mathematics/2014 June 12

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June 12

Nomenclature for deducible knowledge

This questions pertains to logic, which is at an awkward gap between a few different reference desk categories. I hope the mathematically inclined will be interested. —JL

Consider, if you will two cases:

1. If person reading an alphanumeric sequence rendered in an unfamilar typeface encounters a slashed zero, she will readily recognize it as the numeral '0' rather than the letter 'O' because an 'O' is never slashed. However, if she instead encounters a different alphanumeric sequence that contains the letter 'O' but no numeral '0' to compare it against, it may be impossible for her to know with certainty which character she is reading, because a '0' may be drawn with or without a slash and she has no way of knowing which to expect.
2. If a person with no prior knowledge of U.S. state abbreviations encounters the abbreviations 'MD' and 'MT', she will be able to deduce that 'MD' is Maryland and 'MT' is Montana because no other state names fit either of these two abbreviations. However, if the abbreviation she encounters is 'MA', she must (at a minimum) have enough additional information to rule out Maine and Maryland before she can determine that 'MA' is Massachusetts.

Is there a name for this general logical condition where some conclusions may be drawn with limited knowledge while other conclusions of a similar scope require more or complete knowledge? Is there a proper name for optimizing a system to function with the least possible knowledge? —jameslucas (" " / +) 18:59, 12 June 2014 (UTC)

I submit that the person in case 1 is reading a text in Danish, and the person in case 2 does not have enough information to conclude whether MT is Massachusetts or Montana, no matter which other abbreviations are revealed. However, I think the sort of thing you're driving at is peculiarly related to the question of whether a given grid has a Sudoku solution. AlexTiefling (talk) 22:22, 12 June 2014 (UTC)

I don't believe that there is a specific name for this. It also depends on what exactly you mean, for example, in case 2:

1. Am I given a list of abbreviations and told that they are such?
2. Do I know if the abbreviations do "nonstandard" things (like writing Xmas because "X" looks like the Greek chi)?
3. Do I know that they abbreviate states, as opposed to just knowing that they abbreviate; or some partial information of that nature?
4. etc.

It sounds, to me, like you are describing something like Sudoku; or that you are describing looking for a "best fit" meaning/explanation, as in a detective reasoning from clues. You may want to check out some of the following articles, they won't give a name to this, but they do touch on some of the reasoning that may be involved or things relating to that end: Heuristic, Abductive reasoning, Default reasoning, Grammar induction. --If you do have a large enough set of information, though, then it is just plain old deduction; you just can't deduce every relation (As in you can deduce that "MA" must refer to one of the three states, but you can't narrow it down).Phoenixia1177 (talk) 04:40, 13 June 2014 (UTC)

You might want to and the term inference to the list. However, the qualification "... while other conclusions of a similar scope require more or complete knowledge" applies to almost every context where one looks, so it is the default condition and thus hardly needs a name; one simply can deduce has more complete/specific information about some cases than others. —Quondum 21:16, 15 June 2014 (UTC)

Optimisation of state abbreviations

Following on from the subject above, I find myself wondering: are the USA two-letter state abbreviations optimal?

The constraints appear to be that each should have the same initial as the full name (and be both initials, for two-word states), and that if a single-word name contains a letter unique among state with that initial, that letter should appear in the abbreviation (hence AZ for Arizona, the only A-state with a Z). However, once those assignments are made, other states may now have letters that are unique among the remainder, and so on. How much of the current list can be arrived at by this procedure? Does including Canadian provinces and Mexican states make the problem easier or harder? Are there any other nations that could be included in such a scheme without breaking it? AlexTiefling (talk) 22:31, 12 June 2014 (UTC)

The US and Canadian postal abbreviations both started in the 1970s with the US altering *one* state abbreviation to make a unique mapping (Nebraska was NB originally, was changed to NE so that Canada could use NB for New Brunswick... Adding in the Mexican states is very hard if you don't change any US/Canadian ones, you *might* be able to get a unique coding things *with* Mexico, but you'd probably end up with very unpalatable abbreviations like CD for Colorado or CI for California. (To the C's you have to add Campeche, Chiapas, Chihuahua, Coahuila and Colima. (CS for Chiapas, CH for Chihuahua, CU for Coahuila, CL for Colima and CP for Campeche? For the M's you have to add Michoacán (MC?),Moreles (MR?), and Mexico (MX), Mexico City can be FD. — Preceding unsigned comment added by Naraht (talk • contribs)

Well, I just tried the method by hand for US states only, and discovered that (apparently) four of the assigned codes are so inapt they'd be better for other states: AL is a better code for Alaska than for Alabama (for which AB or AM would be ideal), MI is a better code for Maine than for Michigan (for which MG would be best), MS is a better code for Minnesota than for Mississippi (for which MP is a shoo-in), and MO is a better code for Montana than for Missouri (for which MR would be best, as among M-states only Maryland also has an R, and any of MD, ML or MY would be distinctive for Maryland). Minnesota is the fly in the ointment: both Maine and Montana are made up only of letters found in 'Minnesota', so once the other M-states are eliminated, MS has to go to Minnesota to distinguish it from both the others, which can then be distinguished from each other.

A further 10 actual abbreviations are not given by the method above, but aren't assigned anywhere else by it either; the remaining 37 (including DC) are all possible outcomes of this method. I'll try again with a longer list in a bit. AlexTiefling (talk) 12:33, 13 June 2014 (UTC)

Yea, the M abbrevs in the US are a mess. I live in Michigan, which is MI, but MI could also stand for Minnesota, Missouri or Mississippi. I agree that MG would be a better choice for Michigan, as would MP for Mississippi, ML for Maryland, and MC for Massachusetts. However, the remaining M states all lack a unique second letter, so I'd go to 3 letter abbrevs for those, giving us:

MD  = Maryland
MC  = Massachusetts
MG  = Michigan
MP  = Mississippi
MIS = Missouri
MIN = Minnesota
MON = Montana
MAN = Maine

Amazingly, MD for Maryland is the only decent current abbrev, which can't be mistaken for another state.

The As are bad, too, with Alaska and Arkansas being a particular challenge. I'd again go to 3 letter abrevs, where needed:

AB  = Alabama
AZ  = Arizona
ALK = Alaska
ARL = Arkansas  ARK surely

Again, only one is currently unambiguous.

For the C's, we could make them all clear without going to 3 letters:

CF  = California
CD  = Colorado
CT  = Connecticut

Yet again, only one is currently unambiguous.

The I's could also be fixed with 2 letter abbrevs, except for one:

IH  = Idaho
IL  = Illinois
IND = Indiana
IW  = Iowa

For the N's, some current abbrevs are good. North Dakota should be changed to NT, as ND could be confused with Nevada. I'd change Nebraska from NE to NB, but that conflicts with New Brunswick, so 3 letters are needed there. Similarly, NY could also stand for New Jersey, so I'd go to 3 letters there, and NM could stand for Northern Mariana Islands:

NBA = Nebraska	
NV  = Nevada	
NH  = New Hampshire	
NJ  = New Jersey	
NX  = New Mexico	
NYK = New York
NC  = North Carolina	
NT  = North Dakota

The O's are decent, but Ohio should not be OH, as that could mean Oklahoma, too:

OI  = Ohio
OK  = Oklahoma	
OR  = Oregon

The W's could use some tweaking, too:

WG  = Washington
WV  = West Virginia
WC  = Wisconsin
WY  = Wyoming

The rest of the states and DC have unambiguous abbrevs already. US territories are problematic, though, as the current AS for American Samoa is ambiguous with Alaska and Arkansas, MP for Northern Mariana Islands is ambiguous with Mississippi (and what's the P for anyway ?), and VI for the US Virgin Islands is ambiguous with Virginia. Here are my suggestions:

AC  = American Samoa
GU  = Guam	
NMI = Northern Mariana Islands
PR  = Puerto Rico
UV  = U.S. Virgin Islands

About 26 of the current US abbrevs are ambiguous, just within the US alone, and that seems unacceptable, to me. An alternative to going to 3 letter abbrevs to avoid ambiguity would be to go to numbers, like M1, M2, etc., but this would require using a look-up table to figure out which states those were, as you couldn't reason it out anymore. So, while having 2 letter abbrevs might be a nice goal, the way it makes so many of them ambiguous just doesn't seem worth saving a letter, to me. With 3 letters, we can probably not only provide unambiguous US abbrevs, but also toss in Canada and Mexico, and maybe more. StuRat (talk) 16:29, 14 June 2014 (UTC)

It turns out all the Canadian abbreviations on their own are unimprovable. However, when combined with the US ones, AE or AT would be a better choice than AB for Alberta; but including Ontario in the mix improves the usefulness of OH for Ohio. AlexTiefling (talk) 13:04, 13 June 2014 (UTC)