  Categorial type logics, pioneered by Lambek, seek a proof-theoretic
understanding of natural language syntax by identifying categories with
formulas and derivations with proofs. We typically observe an intuitionistic
bias: a structural configuration of hypotheses (a constituent) derives a single
conclusion (the category assigned to it). Acting upon suggestions of Grishin to
dualize the logical vocabulary, Moortgat proposed the Lambek-Grishin calculus
(LG) with the aim of restoring symmetry between hypotheses and conclusions. We
develop a theory of labeled modal tableaux for LG, inspired by the
interpretation of its connectives as binary modal operators in the relational
semantics of Kurtonina and Moortgat. As a linguistic application of our method,
we show that grammars based on LG are context-free through use of an
interpolation lemma. This result complements that of Melissen, who proved that
LG augmented by mixed associativity and -commutativity was exceeds LTAG in
expressive power.
