Details
I am already familiar with Chart Parsing using Earley Parsers. I am however, unsure about whether there even is a meta-syntax like Backus-Naur Form (BNF) that can represent a Context-Sensitive Grammar (CSG). Since parsing using a Linear Bounded Automaton is non-deterministic, I understand that it may be very inefficient.
Goal
My goal is to create a Probabilistic Context-Sensitive Grammar generator from a corpus (in the same fashion as a PCFG). Ambiguous grammars will handled by generating parse forests and possibly utilizing something like SPPF if there is an equivalent of Earley Parsers for CSGs.
What I've Tried
I was recommended ABNF, but it's not obvious if it supports CSGs. Another recommendation was to use Dependency Parsing instead of Constituency Parsing. But that is an entirely different approach from what I want to solve.
This answer seems to indicate that simply simulating an LBA with backtracking is enough. However, again that seems incredibly inefficient.