Finite Restricted Powerset Models for the Lambek Calculus and Its Extensions

Lafont 11] gives an elegant proof of nite model property (fmp) for Multiplicative-Additive Linear Logic (MALL) and suggests it can be adapted to noncommutative linear logics of Abrusci 1]. In 4, 6, 9], fmp for certain fragments of MALL (e.g. BCI, BCII^]) and weaker systems (e.g. the product-free Lambek calculus) has been proven by a diierent method; whereas Lafont uses phase space models and quotient-structures, I employ coonite powerset models and so-called barriers. In this paper I present proofs of fmp by the method of barriers ; I simplify and generalize earlier approaches and use nite restricted powerset models instead of coonite powerset models. The former seem to be more intuitive than the latter as partial models of natural language in the sense of Categorial Grammar 7, 8].