Modal logic of traffic signs

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Sent in by Michael Robinson:

I saw this traffic sign in Toledo, Ohio. Luckily I wasn't driving a truck, or I would have had no idea what I was allowed to do. Since we were in a car, we figured U-turns must be OK. Because we were heading to a place that sold coffee, and nothing must stand between us and our morning latte.


I'm not sure that Michael was in the clear. Working out his concern in more detail, the full deontic-logic table for this sign is

Other Vehicles Trucks
Left Turn  ?  ?
U Turn  ?  NO
No Turn  ?  ?

The sign could mean that U-turns by trucks are forbidden — and by Gricean implication, the other five conditions are allowed. Or it could mean that trucks are not allowed to make any turns, and no vehicles are allowed to make U-turns.

Or …

Anyhow, according to Ohio Laws and Rules 4511.36 Rules for turns at intersections:

(C) The department of transportation and local authorities in their respective jurisdictions may cause markers, buttons, or signs to be placed within or adjacent to intersections and thereby require and direct that a different course from that specified in this section be traveled by vehicles, streetcars, or trackless trolleys, turning at an intersection, and when markers, buttons, or signs are so placed, no operator of a vehicle, streetcar, or trackless trolley shall turn such vehicle, streetcar, or trackless trolley at an intersection other than as directed and required by such markers, buttons, or signs.

So there's that.

And Internet search turns up this troubling item on amazon.com:

Perhaps a broader version of this traffic-sign semantics puzzle will play a role in Dan Brown's next semiotic thriller.

 

 



31 Comments

  1. MattF said,

    August 22, 2016 @ 7:37 am

    I recall a heavily signed multi-road intersection near where I grew up– on the approach from a side street, the only visible signal was a WALK/DONT WALK light. The standing local joke was that you had to get out of your car and walk when you saw it.

  2. Zlatan Ibrahimowizc said,

    August 22, 2016 @ 7:39 am

    Do they test any of this stuff on actual people who don't work for the state?

    In fact, what is the purpose of the "Left Turn Signal" sign? That signal seems pretty self-explanatory since it gives left arrows.

  3. bks said,

    August 22, 2016 @ 7:49 am

    Don't miss Donald Knuth's collection of diamond signs:
    http://www-cs-faculty.stanford.edu/~uno/diamondsigns/diam.html

  4. Adrian said,

    August 22, 2016 @ 8:41 am

    To me the sign is saying "No trucks, no U-turns", so I wouldn't dare to do a U-turn there, though on reflection it's hard to put my finger on how that would/wouldn't make sense.

  5. Robert Coren said,

    August 22, 2016 @ 8:53 am

    I have no idea what to make of those combined arrows. Well, I have a sort of an idea, if the sign is clearly over a lane other than the extreme left: "No left turns or U-turns from this lane". But I would think that it would hardly need saying.

    [(myl) The original wider-angle photo shows that there are only two lanes, and this sign is over the center-right of the left-hand one.]

  6. D.O. said,

    August 22, 2016 @ 9:02 am

    Should it be "No truck U-turns"? For other streetcars or trackless trolleys U-turns (and left turns) are allowed and even the must, that's what depicted on the sign.

  7. John Roth said,

    August 22, 2016 @ 9:24 am

    Clearly left turns are permitted from the leftmost lane – that's the standard meaning of a traffic light with a left arrow, which is simply reinforced by the "left turn signal" sign. We don't need to invoke Gricean implication for that. As far as the other sign, I'd go with the meaning that prohibits trucks from making U-turns; if they wanted to prohibit trucks from making any turns, they would just say that. If they wanted to prohibit anyone from making U-turns, they wouldn't use this visual, which explicitly allows at least some kinds of vehicles to make U-turns.

    The one that bugs me is the "no turn on red" sign near where I live that's placed so it's behind the car at the front of the right turn lane.

  8. Bob Ladd said,

    August 22, 2016 @ 9:45 am

    I read this as PERMITTING U-turns, except for trucks. That is, I think No has scope only over trucks, and the line U-turns is a SEPARATE instruction that amounts to "use the left turn lane also for U-turns". If I'm right about this, then in Mark's table above we need a "NO" under Trucks in the Left Turn row as well.

    Also, question for MYL: What would you understand by "YES" and "NO" in the third row of your logic table?

    [(myl) "YES" would mean it's OK to go straight; "NO" would mean it isn't, as sometimes happens when a two-way street becomes one-way (in the wrong direction).

    Don't forget that we're talking about modal logic, not common sense…]

  9. George Grady said,

    August 22, 2016 @ 10:11 am

    There's a yellow diamond sign on US-19 between Capps and Perry in Florida that reads "HILL BLOCKS VIEW". As hills aren't generally known for their transparency, it's always seemed not to be terribly informative to me.

  10. majolo said,

    August 22, 2016 @ 10:12 am

    Maybe it's just missing a bit of Hutzian punctuation: "No! Trucks, no U-turns!"

  11. Steve Kass said,

    August 22, 2016 @ 10:14 am

    Google Street View shows the approach to this intersection. https://goo.gl/maps/ezpd6AoWWzP2 The overhead signs seem to apply to the lane in the right foreground with left/U-turn arrow painted on it. (The word ONLY is painted on this lane further back.) What’s painted on the lane supports the interpretation “U-turn or left turn only from this lane, but no trucks may make a U-turn.”

  12. Marion said,

    August 22, 2016 @ 10:29 am

    There's a sign near me in Newmarket, UK – 'Hidden Dips'. Apart from always making me think of concealed guacamole, it's a bit like @George Grady's 'hill blocks view': you might say that if you can't see the dips, you won't realise that an oncoming car might be hidden in one, but I guess it's really the hidden vehicles they're thinking of.

  13. GretchenJoanna said,

    August 22, 2016 @ 11:11 am

    This is simply painful! As if driving isn't already challenging enough.

  14. Guy said,

    August 22, 2016 @ 11:55 am

    Clearly no one can make a left or u-turn, since the left turn arrow is red!

  15. pj said,

    August 22, 2016 @ 12:43 pm

    'Buttons'? What sort of thing do they mean by 'buttons' in that legislation?

    [(myl) I wondered about that too. Internet search suggests that "markers, buttons, or signs" is a legal drafting idiom in the U.S. — at some point someone must have had a notion what a "button" is in this context, but I bet that now drafters are just copying the language from somewhere else.]

  16. wanda said,

    August 22, 2016 @ 3:11 pm

    Some vehicles clearly are allowed to make a U-turn. Otherwise, the U-turn arrow in the sign would have a circular red strikeout graphic thing on it.

  17. Gwen Katz said,

    August 22, 2016 @ 4:11 pm

    The image makes it clear that U-turns are allowed, leaving the only reasonable interpretation that only truck U-turns are forbidden. But "U-Turns No Trucks" would have been much clearer.

    I'm much more confused by "Left Turn Signal." Does it mean that left turns must signal, or is it labeling the light as a left turn signal?

  18. David L said,

    August 22, 2016 @ 4:49 pm

    @George Grady: presumably the thinking behind the sign is that hills are so rare in Florida that drivers need to be reminded of their concealing tendencies.

  19. Will M said,

    August 22, 2016 @ 6:31 pm

    "Buttons" might be referring to what I've always known as "Botts' dots": https://en.wikipedia.org/wiki/Botts%27_dots

    I don't remember seeing these used to prohibit turns per se, but they are used in place of lane marker paint, and I suppose the double yellow "do not cross ever" pattern also prohibits turns that cross it.

  20. PaulB said,

    August 22, 2016 @ 7:15 pm

    As I read it, it simply(!) says that 'NO TRUCKS' are allowed in the turn lane; and that 'U-TURNS' are permitted at this intersection.

  21. PS said,

    August 22, 2016 @ 8:03 pm

    The Border Roads Organization, an Indian government agency responsible for the upkeep of the treacherous mountain highways in the Ladakh region near the Indo-Chinese border in Jammu and Kashmir, has become quite popular in India for its often wacky, sometimes poetic signage. There is even a book about them now: http://ladakhroadsigns.com/

    Some samples:

    1) Let your insurance policy mature before you.

    2) Drive on horse power not on rum power.

    3) Left is right, right is wrong. (Indian highways follow left hand drive).

    and so on.

  22. PS said,

    August 22, 2016 @ 8:08 pm

    Their Wikipedia page seems to have even more amazing signs: https://en.wikipedia.org/wiki/Himank

  23. Robert Coren said,

    August 23, 2016 @ 9:46 am

    Gwen Katz: It's labelling the light. Such signs are fairly common.

  24. John Swindle said,

    August 23, 2016 @ 10:39 pm

    The sign would be clearer if it said "TRUCKS NO U-TURN," but the shape of the sign requires a line break which might be problematic.

    I agree with Will M that roadway "buttons" in law or regulation are probably the same as "Botts Dots." I never knew a name for them. And they'd be part of a range of raised pavement markers (in the American sense of "pavement") used for various purposes.

  25. davep said,

    August 25, 2016 @ 3:37 am

    Gwen Katz: "I'm much more confused by "Left Turn Signal." Does it mean that left turns must signal, or is it labeling the light as a left turn signal?".

    You shouldn't be. You are required to use your vehicle's signal for every left turn anywhere (not just at places with this sign). The sign refers to the traffic light (it's used at other locations). I suspect the light isn't always an arrow. When the light is a full red (not a red arrow), the sign indicates that people turning left need to wait for a green left arrow).

  26. davep said,

    August 25, 2016 @ 3:57 am

    PaulB: "As I read it, it simply(!) says that 'NO TRUCKS' are allowed in the turn lane; and that 'U-TURNS' are permitted at this intersection."
    No.

    The double headed arrow (already) indicates U-turns (and left turns) are allowed.

    Keep in mind that the signs are read from top to bottom.

    The general case is listed at the top and the exceptions are listed following.

    Your interpretation of the "U-turn" text at the bottom would make that text redundant. I'll suggest that redundancy doesn't really ever occur or it's quite rare (meaning expecting redundancy isn't a useful tactic for interpretating traffic signs). For your interpretation, "no trucks" alone would have been sufficient (and more clear).

    It might have been better to say "No truck / U-turns" (it's the pluralization of "truck" that makes it confusing). Or "No U-turns/for Trucks" ("/" indicates a line break).

  27. davep said,

    August 25, 2016 @ 4:24 am

    Mark Lieberman: "I'm not sure that Michael was in the clear."

    The double-headed arrow at the top of the sign indicates fairly-clearly that two types of turns are allowed (left turns and U-turns). The double-headed arrow, itself, is not very common (that's part of why some people are confused).

    Traffic signs don't often (ever?) repeat themselves.

    Expecting redundancy is not a useful heuristic tactic for interpretating traffic signs.

    The arrow at the top already says U-turns are allowed.

    One should expect the rest of the sign is saying something else (not repeating itself).

    Michael Robinson (quoted in the post): "Since we were in a car, we figured U-turns must be OK."

    This indicates that he suspected it could have been was "no U-turns" for all vehicles, which would make the sign contradict itself. Expecting contradiction is really never a useful heuristic tactic. Nor is expecting the sign to have an error very useful.

    Anyway, if it was "no U-turns" for all vehicles, it would have been "/No U-turns/No Trucks".

  28. BZ said,

    August 25, 2016 @ 12:54 pm

    For everyone insisting that the diagram clearly means that U-Turns are ok, I have to disagree. This is clearly a nonstandard sign. Usually a U-Turn is always allowed where a left turn is allowed absent a "No U-Turn" sign, either in text or turning arrow with a (usually red) slash over it. This is true even when there is an "only" with a left turn arrow (or like here where "left turn signal" and a signal with only left arrows). Sometimes, a sign such as above (but without any text) does mean to reinforce that U-Turns are permitted, in case it is non-obvious.

    If the meaning is that trucks cannot make U-Turns (but other vehicles can), the diagram should have been left out and the text reworded. It is already clear that some vehicles can turn left (hence the signal). The re-worded sign would make clear that other vehicles can make a U-Turn (hence the trucks).

    Therefore, the diagram might be construed as telling you what the trucks cannot do, though the text is wrong then. Maybe the text on the sign should say "except trucks", which would make the intent perfectly clear.

    If the sign meant "no trucks, no U-Turns", maybe the diagram is telling you what the trucks cannot do. In such a case "No U-Turns" should be on a separate sign and "No Trucks in this lane" should make the diagram unneeded.

    On the other hand, the diagram might be saying what the trucks *must* do. "No Trucks" would mean straight ahead. All trucks must turn left or make a U-Turn. Then, only trucks are allowed to make a U-Turn here due to the fact that they don't have much other choice. This case would also much better be handled by two separate signs, one saying "No U-Turns except Trucks" and another saying "No trucks beyond this point"

  29. davep said,

    August 26, 2016 @ 12:32 am

    BZ: "For everyone insisting that the diagram clearly means that U-Turns are ok, I have to disagree. This is clearly a nonstandard sign."

    The double-headed arrow shows what sort of turns are allowed. That might be "nonstandard" but it certainly doesn't indicate that left turns or U-turns are not allowed. Clearly, left turns are allowed and the double-headed arrow points to the left. That it also shows a U-turn can only mean U-turns are allowed too.

    People see the double-headed arrow as being unfamiliar and they choose to pretend it doesn't exist.

    BZ: "Sometimes, a sign such as above (but without any text) does mean to reinforce that U-Turns are permitted, in case it is non-obvious."

    The arrow is doing the same thing here.

    It's "left turns and U-turns are allowed except trucks can't make U-turns".

    Your interpretation is much too complicated! It's much more likely to have a simpler interpretation.

    BZ: "Therefore, the diagram might be construed as telling you what the trucks cannot do, though the text is wrong then."

    If your interpretation leads to the conclusion that the "text is wrong", that tends to invalidate the interpretation!

    It's much more reasonable to choose a simpler interpretation that doesn't lead to a contradiction.

  30. davep said,

    August 26, 2016 @ 12:38 am

    BZ: "On the other hand, the diagram might be saying what the trucks *must* do. "No Trucks" would mean straight ahead. All trucks must turn left or make a U-Turn. Then, only trucks are allowed to make a U-Turn here due to the fact that they don't have much other choice. This case would also much better be handled by two separate signs, one saying "No U-Turns except Trucks" and another saying "No trucks beyond this point""

    This is confusing. In any case, it leads to the "text being wrong" too. All this isn't likely to be the intent.

    It'simply "left turns and U-turns are allowed except trucks can't make U-turns".

  31. FM said,

    August 29, 2016 @ 2:43 pm

    I'm with PaulB. In view of "nerdview", I would interpret it as a list of properties of this left turn lane:
    – no trucks
    – yes, U-turns are allowed.
    Yeah, the second part is redundant with the rest of the sign which shows that you can turn both left and around. But that's just the sort of pedantry that I would expect from traffic engineers.

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