Minimalist Grammar: Construction without Overgeneration
Isidor Konrad Maier Johannes Kuhn Jesse Beisegel Markus Huber-Liebl Matthias Wolff
In this paper we give instructions on how to write a minimalist grammar (MG).
In order to present the instructions as an algorithm, we use a variant of
context free grammars (CFG) as an input format. We can exclude overgeneration,
if the CFG has no recursion, i.e. no non-terminal can (indirectly) derive to a
right-hand side containing itself. The constructed MGs utilize licensors/-ees
as a special way of exception handling. A CFG format for a derivation
$A\_eats\_B\mapsto^* peter\_eats\_apples$, where $A$ and $B$ generate noun
phrases, normally leads to overgeneration, e.\,g., $i\_eats\_apples$. In order
to avoid overgeneration, a CFG would need many non-terminal symbols and rules,
that mainly produce the same word, just to handle exceptions. In our MGs
however, we can summarize CFG rules that produce the same word in one item and
handle exceptions by a proper distribution of licensees/-ors. The difficulty
with this technique is that in most generations the majority of licensees/-ors
is not needed, but still has to be triggered somehow. We solve this problem
with $\epsilon$-items called \emph{adapters}.