Bio-inspired cognitive modeling or cognitive modeling?

Our lab haven't started yet and there was huge discussion about the name. Surely it is very important what will your name be. But what is interesting is that the discussion wasn't about the personal preferences but it went deeper.

We have discussed whether it is even possible to talk about cognitive modeling as bio-inspired cognitive modeling. Is cognition only functionalism phenomenon independent on the substrat or is it strictly biological phenomenon?

When we see it from the functionalism view then we focus on the functional ralations and it can be realized also in the robotics environment. Bio-inspired cognitive modeling is possible.

But there is also other point of view when we consider cognition as a strictly biological phenomenon. So it is allways related to the biological reality and bio-inspired cognitive modeling is nonsense (or at least repeated information). Because bio-inspiration could mean that we only construct some artificial system which isn't model in the real meaning - there is nothing to validate. From the model which isn't real system I can't also get inspiration how does the real biological system work.
Or does bioinspiration mean that we are constructing models which are trying to be nearly as complex and universal as the brain functioning is?

Does exist cognitive modeling which isn't bio-inspired? Something like we try to model cognition in the robot without any knowledge of the human brain? Is it still cognitive modeling?

So what will we be focused on?
What is bio-inspiration, cognition, intelligence? Too many words which have nearly lost their specific meaning and are nowdays used as something very fuzzy.
(this was mainly discussed by Matěj Hoffman and Michal Vavrečka)

We have searched the google and I have found also conference which name was "Bio-inspired modeling of cognitive tasks". So there are at least different interpretations. Or is it misused in this case?

Further Matěj mentioned the article from Barbara Webb: "Animals versus animats: or why not model the real iguana", where she compares artificial models and real animals or artificial systems exactly copying the biological systems.

So we decided to use as the name of the group something less controversial: Cognitive modeling and bio-inspired robotics.

Nice, nice, nice. Haven't started yet and so nice discussion. Looking forward:-).