5 problems

Consider extending the cut-elimination proof for the multiplicative-additive Lambek calculus with subexponential and bracket modalities, which uses “deep cut elimination” for $!$-f…

Completeness conjecture. An axiomatization for the one-variable fragment of the first-order version of full Lambek Calculus should be complete for valid equations, but not for cons…

Let $\boldsymbol{!}_{\mathbf{b}}^{\mathbf{2015}} \mathbf{MALC^{\boldsymbol{*}}b}\mathrm{(st)}$ be Morrill's first bracketed system, and consider sequents obeying the bracket non-ne…

Product-elimination conjecture. The product can be eliminated completely: one can prove $\Pi_1^0$-hardness for

The paper considers the Lambek calculus with brackets and unit, denoted here by $\mathbf{Lb}^{\boldsymbol{*}}_{\mathbf{1}}$, together with its multimodal version. The construction…