Perfect Simulation - Unless given specific and compelling reason to believe otherwise, we operated under the assumption that the Matrix is a nigh perfect simulation of the real world. Mirroring real world physics right down to the atomic level. This applies to the macro level too, of course. Society and life at large should operate as we know it as default.

Machines Are Not Omniscient - Generally speaking, we assume that things go on in the Matrix autonomously. If life was under complete observation, we choose to assume that no hackers should exist inside the Matrix. The machines do not have perfect knowledge.

No Mind Control - The machines do not have the ability to easily control, read, or alter the mind. Thomas Anderson's interview would have gone much differently if they did.

They Are Not Liars - The characters in The Matrix are generally assumed to be speaking the truth... if not in the absolute sense. They may be speaking from a specific or limited perspective or speaking figuratively, so interpretation is necessary, but we presume their statements to be true.

The Oracle's Residence - For all intents and purposes of this site, The Oracle lives in the Matrix. Whether she specifically does or not is somewhat irrelevant to this site. Her apartment has many elements of permanence and is accessed through the Matrix by the crew. For illustrative purposes, like always, unless given specific or compelling evidence otherwise, we'll use this postulate.

Proofs
try to realize the truth

The Oracle is A Machine - Joel Silver said as much in Premier Magazine. This also demonstrates that there are good machines. The Animatrix and other Reloaded previews confirm this.