The BDI element is currently described as follows:

> The bdi element represents a span of text that is to be isolated from its
> surroundings for the purposes of bidirectional text formatting. [BIDI]
> [...]
> For the purposes of applying the bidirectional algorithm to the contents of a
> bdi element, user agents must treat the element as a paragraph-level container.
>
> For the purposes of applying the bidirectional algorithm to the paragraph-level
> container that a bdi element finds itself within, the bdi element must be
> treated like a U+FFFC OBJECT REPLACEMENT CHARACTER (in the same manner that an
> image or other inline object is handled).

This description was based on the spec for unicode-bidi:isolate (http://www.w3.org/TR/2012/WD-css3-writing-modes-20120501/), through which BDI is implemented:

> For the purposes of the Unicode bidirectional algorithm, the contents of the
> element are considered to be inside a separate, independent paragraph with a
> base directionality given by the element's ‘direction’ property, and for the
> purpose of bidi resolution in its containing bidi paragraph (if any), the
> element itself is treated as if it were an Object Replacement Character
> (U+FFFC).

However, due to the subsequent addition of bidi isolates to Unicode (on track for Unicode 6.3), the inability of Unicode isolates to span across a paragraph break, and the desire to base CSS isolates on Unicode isolates, the CSS definition had to be modified (http://www.w3.org/TR/2012/WD-css3-writing-modes-20121115/):

> On an inline element, this bidi-isolates its contents. This is similar to a
> directional embedding (and increases the embedding level accordingly) except
> that each sequence of inline-level boxes uninterrupted by any block boundary
> or forced paragraph break is treated as an isolated sequence:
> * the content within the sequence is ordered as if inside an independent
> paragraph with the base directionality specified by the element's ‘direction’
> property.
> * for the purpose of bidi resolution in its containing bidi paragraph, the
> sequence is treated as if it were a single Object Replacement Character
> (U+FFFC).
> In effect, neither is the content inside the element bidi-affected by the
> content surrounding the element, nor is the content surrounding the element
> bidi-affected by the content or specified directionality of the element.
> However, forced paragraph breaks within the element still create a
> corresponding break in the containing paragraph.

The new CSS definition, and especially the note about forced paragraph breaks within the element (e.g. BR), should be reflected in the HTML spec of BDI.