TL;DR - see proposal

CSS Cascade says

The inherited value of a property on an element is the computed value of the property on the element’s parent element. [...]
Note: Inheritance follows the document tree and is not intercepted by anonymous boxes

It says "parent element" and "document tree", but both CSS Selectors and CSS Pseudo-elements seem to override this for ::first-line:

During CSS inheritance, the portion of a child element that occurs on the first line only inherits properties applicable to the ::first-line pseudo-element from the ::first-line pseudo-element. For all other properties inheritance is from the non-pseudo-element parent of the first line pseudo element.

However, browsers do strange things (https://jsfiddle.net/0geoep6t/)

<div>
  <span>ABCDEFGHIJKLMNOPQRSTUVWXYZ</span>
</div>

div {
  color: blue;
  background: yellow;
  border: 10px solid blue;
}
div::first-line {
  color: red;             /* Applies and is inherited by default */
  background: cyan;       /* Applies and is not inherited by default */
  border: 10px solid red; /* Does not apply to ::first-line */
}
span {
  color: inherit;         /* Firefox, Edge and Chrome inherit from ::first-line */
  background: inherit;    /* Firefox and Edge inherit from div, Chrome from ::first-line */
  border: inherit;        /* Firefox and Edge inherit from div, Chrome from ::first-line */
}

If I understand correctly, since background applies to ::first-line, background: inherit should inherit from the ::first-line, like Chrome does. And since border does not apply to ::first-line, border: inherit should inherit from the div, like Firefox and Edge do.

Am I right? Consider adding some note to the spec to clarify this.