It is well known that unification based grammar formalisms are Turing-equivalent in their generative capacity (Pereira and Warren, 1983;Johnson, 1988, 87-93); determining whether a given string ¡ is generated by a given grammar is equivalent to deciding whether a Turing machine halts on an empty input, which is known to be undecidable.
the recognition problem is undecidable in the general case.