What are constraints on some new logic programming language and system?
It sounds like you have the impression that there are some rules on what languages you are allowed to define.  There are no such rules.  You can define whatever language you want.  You can do whatever what you want -- you're not required to do anything (there are no language police who will come arrest you for failing to prove some theorem about it).  Whether it will be useful, or used by anyone else, is a different matter.