Well, if you have two facts and you want to combine them, then they need to contain the same set of dimensions. Imagine you have two facts - cars and people. Cars have a num_wheels dimension and people have a hair_colour dimension. It makes no sense to report how many people have four wheels!!
You can actually combine facts at different dimensionality though using the FILTER clause. See here: Combining Facts/Subject Areas in Oracle OBIEE - Part 2 - Beyond Blog
OBI at ist core is a source agnostic query Generator for any source there is.
Logical dimensions and Logical Facts are - as their "Logical" bit of the Name implies - actually completely artificial concepts and have Zero to do with the physical model in the strictest sense of the word. I can happily and easily create a 10 fact, 30 Dimension model where only 4 dims will ever be conformed on one single flat file.
You must comprehend this to comprehend why OBI does things the way it does them.
a) all business model concepts are virtual
b) don't even think "this Logical Dimension just means a dimension table" - through multiple LTSs and multiple tables nested inside each LTS I can create you a "Dimension" which - while a logical entity - is sourced from 20 physical sources, 2 being tables, 4 being cubes, 11 being XML and 3 coming from Hadoop
Yes this is the strongest feature of the NQuire Server which people still don't get comprehend 20 years after its inception.
Every fact has a dimensional context
Every dimensional attribute is related through a fact (conformed dimensions & implicit facts)
Use of information drives fact star design (typically a related set of business questions are answered by a single fact star)
+ to Christian Berg
^ the basic rules
True, but contrary to breathing and heartbeat they don't happen automagically