Could computers invent language?

Artificial intelligence is something about which not a line has been written in these pages in next to two hundred posts and over more than ten years. But I feel today like I should drop a couple of thoughts about it, after exchanges on Google+ around this post by +Gideon Rosenblatt and that one by +Bill Slawski, not to mention recent fears expressed by more famous people.
There are many definitions of artificial intelligence, and I will not quote or choose any. Samely, popular issues I also prefer to let alone, like knowing if computers are able to deal only with data and algorithms, or if they can produce information or even knowledge, or if they think and can individually or collectively accede to consciousness or even wisdom. All those terms are fuzzy enough to allow anyone to write anything and its contrary on such issues. Let's rather look at some concrete applications.
Pattern recognition is one of the great and most popular achievements of artificial intelligence. Programs are now able with quite good performance to translate speech into written language, identify music tracks, cluster similar news, identify people and cats on photographs etc. 
Automatic translation is also quite popular, and working not that bad for simple factual texts, has still hard time dealing with context to solve ambiguity, understand puns and implicit references, all things generally associated with intelligent understanding of a text. 
Question-answering is also making great progress, based on more and more rich and complex knowledge graphs, and translation of natural language question into formal queries.
No doubt algorithms will continue to improve in those domains, with many useful applications and some related and important issues regarding privacy and delegation of decision to algorithms.

All the above tasks deal more or less with the ability of computers to process successfully our languages. But, and this is where I'm bound from the start, there is a fundamental capacity of human intelligence which, as far as I know, has not even began to be mimicked by algorithms. It's the capacity to invent language. It has been largely discussed since Wittgenstein whether a private language is possible or not, but there is no discussion that language has been and still is built collectively through a proceess of collective continuous invention. Anyone can invent a new word or a new linguistic form; whether it will be integrated into the language commons depends of many criteria akin to the ones enabling a new species to expand and survive or disappear. This is the way our languages constantly evolve and adapt to the changing world of our communication and discourse needs. Could computers be able to mimick such a process, take part in it, and even expand it further than humans? Could algorithms be able to produce new and relevant words, smoothly integrated in the existing language, to name concepts not yet discovered or named? In short, are computers able to take part in the continuous invention of language, and not only make a smart use of the existing one?
Such a perspective would be indeed fascinating and certainly scary, insofar as machines inventing collectively such language extensions would not necessarily share them with humans, and even if they do, humans would not necessarily be able to understand them

Whether such an evolution is possible at all or in a foreseeable future is a good question. Whether we should hope for it and work to let it happen, or should fear and prevent it, is yet a more interesting one. But at the very least, those questions we can technically specify, making them much more valuable for assessment and definition of artificial intelligence than vague digressions on whether computers can think, have knowledge or can become conscious. We don't even really know what the latter means for humans, our shared language being the closest proxy we have for whatever is going on in our brainware. So let's assess the progress of artificial intelligence by the same criteria we generally use to assess the human intelligence, its ability to deal with language, from plain naming of things to invention of new concepts.