Sony has an unstable history when it comes to compatibility backwards, starting from accepting the concept until recently releasing it as an unused feature. We've now seen the first details of the PlayStation 5, and they include PS4 compatibility.
Mark Cherny, who was the leading system architect for the PS4, says the next generation PlayStation (which is not yet technically called the PlayStation 5) uses a similar architecture to its predecessor, allowing this feature. It will also use physical disks, and Cerny expects some games to be released via both consoles.
However, PS4 games will work a bit faster on the PS5, thanks to the inclusion of a solid state (SSD). As an example, Cerny compared the loading times for a quick trip to Spider-Man. The PS4 Pro load lasted about 15 seconds, but the same sequence lasted less than a second on the PS5 Dev kit. So, if you upgrade your hardware, you will probably have a nice boring experience in some ways.
We still do not know exactly how far the next generation of PlayStation can be. Last year, PlayStation head John Coeur suggested that the new system remain for three years. That would mean it's two years away, so neither Sony is preparing a long launch pad or the schedule is significantly accelerated.