Non-associative Lambek calculus with modalities: interpolation, complexity and FEP

We obtain some results on interpolation, complexity and FEP for modal extensions of Non-associative Lambek Calculus, admitting modal axioms T, 4, 5. These results extend earlier ones from W. Buszkowski (2005, CSLI Publications, 77–93; 2011, Log. J. IGPL, 19, 437–454; 2009, LNCS: 5533, 45–58), not admitting these axioms.