Does anyone know which おり this is?

Question

彼女は表情が生き生きとしておりとてもかわいい。

was translated awkwardly on ALC as

She is very pretty for the liveliness of her expression.

Which おり is this? I think I know it from the polite しております　but is it here wielding more expressive meaning?

Answer 1

It replaces the verb stem い (of いる) for morpho-phonological reason.

The construction in your example uses a verb stem to continue another predicate after it as in:

よく食べ、よく寝る。 [Vowel verb stem 'tabe']
年月が経ち、忘れてしまった。 [Consonant verb stem 'tat' followed by the epenthetic vowel 'i']

When you use the verb いる in this construction, its stem 'i' is very short that some people don't like it, and may even consider it ungrammatical:

生き生きとしてい、とてもかわいい。

Those people replace i with a longer verb stem or, which can be considered in present Japanese a variant of this verb stem:

生き生きとしており、とてもかわいい。 [Consonant verb stem 'or' followed by the epenthetic vowel 'i']

When it is followed by an affix, the shortness of the stem is compensated by the affix, and it does not sound bad, so both forms are allowed:

...しています。
...しております。

Translation

The translation that you got is a good one for a literal translation.

　彼女は表情が生き生きとしており、とてもかわいい。
　'As for her, the facial expressions being lively, she is very pretty.' (Literal)
　'Her facial expressions are lively, which make her very pretty.' (Natural)

Answer 2

Let me have a go at this:

• 彼女{かのじょ}は: She/Her (establishing context)

• 表情{ひょうじょう}が: expression (with nominative case marker)

• 生{い}き生{い}き: vividly, lively

• して: Verb conjunctive form of する

• おり： 連用形 of　居る{おる} (To be/exist for animate things) This should be the verb you're looking for

• とても: intensifier

• かわいい：　pretty

1. The verb is 生き生きとして居る, the subject is 表情. Combining them yields "There is a vivid/lively expression"

2. Context is 彼女

   Combining 1. and 2. yields "For her, there is a vivid lively expression"

Now put the verb in 連用形 to get:

3.彼女は表情が生き生きとしており

One of the uses of the 連用形 is to join up several sentences as subphrases into a large continuous sentence.*

One sentence has been established, which is in 3.彼女は表情が生き生きとしており

The other sentence is とてもかわいい ((She) is very pretty)

Combining them yields "She has a lively expression, she is very pretty"

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EDIT: Regarding your comment on trying to introduce a "because" nuance.

You can use the　て-form of the verb to introduce an implicit sequence of events. (Weak causal relation)(If you want a stronger causal relation, use から)

See Verb Grammar - The Verb Conjunctive Form(You have to scroll down a little bit)

The difference between linking sentences with て-form and　linking with 連用形 is that there is no implicit sequence of events when linking with 連用形.

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*Extracted from nihongoresources:

One of the uses of the 連用形 is to join up several sentences as subphrases into a large continuous (which is what 連用 means) sentence, similar to how in English for instance you would join up two sentences by putting a comma between them and if necessary changing the phrasing on the first sentence just a tiny bit. If we look at an example you might get an idea of how this works:

日本語：　花が咲く。 English: Flowers bloom.

日本語：　鳥が鳴く English:　Birds are chirping..

日本語：　春が来た。 English:　Spring has come.

We can combine these into a single sentence:

日本語：　花が咲き鳥が鳴き春が来た。 English:　Flowers bloom, birds are chirping; spring has come.