transaction log restore we have an external production database (maintained by another company) and we are trying to build an internal database that replicates the production database for reporting purposes (both sql-server). 

Here is the scenario: they have sent us a full backup (BAK) which I already have it restored properly. And they will send us the transaction logs (TRL) on a daily basis.

I know I can restore it with BAK plus all the TRL sequentially and overwrite the previous restore. But is there a way that I can restore with the most recent log I received 'incrementally'?

Thanks in advance. And correct me if I used inappropriate terminologies.

:)
It depends on whether your local server is Enterprise Edition. 

If so, you can restore the database backup and leave it in NORECOVERY mode.  You will not be able to directly access the database, but you can create a SNAPSHOT database which will be Read Only.

That snapshot database can be dropped, the new TRL restored in NORECOVERY Mode, and recreate the snapshot.