Isidor Konrad Maier

Isidor Konrad Maier, Johannes Kuhn, Jesse Beisegel et al.

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 $ε$-items called \emph{adapters}.

Isidor Konrad Maier, Matthias Wolff

This paper presents a novel numeral decomposer based on arithmetic criteria. The criteria are not dependent on a base-10 assumption but only on Hurford's Packing Strategy. Hurford's Packing Strategy constitutes numerals by packing factors and summands to multiplicators. We found out that a numeral of value n has a multiplicator larger than sqrt(n), a summand smaller than n/2 and a factor smaller than sqrt(n). Using these findings, the numeral decomposer attempts to detect and unpack factors and summand in order to reverse Hurford's Packing strategy. We tested its applicability for incremental unsupervised grammar induction in 273 languages. This way, grammars were obtained with sensible mathematical attributes that explain the structure of produced numerals. The numeral-decomposer-induced grammars are often close to expert-made and more compact than numeral grammars induced by a modern state-of-the-art grammar induction tool. Furthermore, this paper contains a report about the few cases of incorrect induced mathematical attributes, which are often linked to linguistic peculiarities like context sensitivity.