8 problems

Orthologic is the logic of quantum propositions, while intuitionistic logic is constructive logic; consider the implication-free fragment of intuitionistic logic in the signature…

Consider the $\square$-free fragments and the $\lozenge$-free fragments of the intuitionistic modal logics studied in the paper. Non-finite-axiomatizability conjecture. Either some…

Let $\mathbf{L}_{\min}$ be the minimal intuitionistic modal logic in the language with $\square$ and $\lozenge$, and let $\mathbf{WK}$ be the intuitionistic modal logic in the lang…

Completeness conjecture. A complete axiomatization of $LDC\preceq E$ consists of the following: the proposed axioms and rules form a complete axiomatization of the logic…

Consider the trimodal $d$-logic of dynamical systems based on scattered spaces, where the trimodal language includes the henceforth operator and the tangled derivative. On scattere…

Let $\bold{DGL}$ be the extension of $\bold{GLC}$ that includes the temporal operator $*$. The tangled derivative operator is trivial on scattered spaces, so the original spatial o…

Let $\bold{GLC}$ be the dynamic logic of dynamical systems based on scattered spaces, and let $\mathcal{L}^{\circ*}_\lozenge$ be the trimodal topo-temporal language. Extend…

s$\Delta$M axiomatization conjecture. Replacing $\Delta$M in the axiomatizations of the second-level logics with s$\Delta$M should yield axiomatizations of the logics on the third,…