Jens Michaelis, Uwe Mönnich and Frank Morawietz

Algebraic Description of Derivational Minimalism

Abstract

In this paper we extend the work by Michaelis (1999) which shows how to encode an arbitrary Minimalist Grammar in the sense of Stabler (1997) into a weakly equivalent multiple context-free grammar (MCFG). By viewing MCFG rules as terms in a free Lawvere theory we can translate a given MCFG into a regular tree grammar. The latter is characterizable by both a tree automaton and a corresponding formula in monadic second-order (MSO) logic. The trees of the resulting regular tree language are then unpacked into the intended "linguistic" trees with an MSO transduction based upon tree-walking automata. This two-step approach gives an operational as well as a logical description of the tree sets involved.