13 problems

A semi star-autonomous category is the categorical structure defined in the paper, and a proof-net category is the unitless linearly distributive category with suitable duals defin…

Physical duoidal category conjecture. Physical duoidal categories also form isomix linearly distributive categories.

An LNL polycategory is a polycategory equipped with a linear/nonlinear structure, and an LNL multicategory of Kleisli type is one whose storage modality is bijective on objects. Th…

Skew monoidal closed coherence conjecture. The free skew monoidal closed category on $\mathsf{At}$ corresponds to a skew variant of the $(\mathsf{I},\otimes,\multimap)$ fragment of…

Let CL, IL, and ILL denote classical, intuitionistic, and intuitionistic linear logic, respectively. Let $\mathrm{LL}^-$ be linear logic without concurrency or polarization. The no…

The authors' approach generalises interpolants to sets of sequents and uses orthogonality to define duality between interpolants. Extension conjecture. This key insight can be exte…

A model of second-order multiplicative linear logic is injective with respect to existential linkings when distinct existential linkings are mapped to distinct elements by the mode…

Consider the relations arising from the different versions of the analytic rules encoding the pairing axioms P1 and BLP2 in the multi-type calculi for linear logic. Positive-fragme…

In bi-intuitionistic linear logic, let $\oc$ denote the exponential connective for necessity and let $\wn$ denote the exponential connective for possibility. Non-interdefinability…

Let $\Omega$ be a perennialization and let $\vn{P}$ be a semi-regular outlook, that is, a semi-regular maximal abelian sub-algebra in the setting of the paper. The notation…

Let $\Omega$ be a perennialization and let $\vn{P}$ be a semi-regular outlook, that is, a semi-regular maximal abelian sub-algebra in the setting of the paper. The notation…

Local-strategy completeness conjecture. The vertical negated edges may be rectified by passing to local strategies in the sense of the cited previous work.

Retractability characterisation. A circuit is the translation of a proof if and only if it is retractable with respect to Maieli's $R_1,\ldots,R_4$ (dropping $R_5$).