A Model-Theoretic Description of Tree Adjoining Grammars1 1The research presented in this paper was supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 441, TP A2. The authors wish to thank Jens Michaelis and Stephan Kepser for helpful comments.
Frank Morawietz, Uwe Mönnich · Electronic Notes in Theoretical Computer Science · 2004
In this paper we show that non-context-free phenomena can be captured using only limited logical means. In particular, we show how to encode a Tree Adjoining Grammar [16] into a weakly equivalent monadic context-free tree grammar (MCFTG). By viewing MCFTG-rules as terms in a free Lawvere theory, we can translate a given MCFTG 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 through a model-theoretic interpretation in the form of an MSO transduction based upon tree-walking automata. This two-step approach gives a logical as well as an operational description of the tree sets involved.