19 problems

Pretransitivity conjecture. If a normal modal logic $\Lambda$ is interpretable by a modal-to-modal translation with parameters in a pretransitive normal logic, then $\Lambda$ is pr…

For each $n$, let \mathcal{F}^n = \langle \mathbb{R}^{1+n}, \mathrel{\scalebox{0.85}{oldalpha}} \rangle be the frame of $(1+n)$-dimensional Minkowski spacetime with causal rela…

Let $n \geq 3$ and let $M$ be a cNTV $n$-dimensional spacetime. Write \langle M, \mathrel{\scalebox{0.85}{oldalpha}} \rangle for its frame with the causal relation…

Let a UCF simplicial model be a simplicial model in the class called UCF in the paper, and let $d53f$ be the logic consisting of propositional logic together with the…

ALUT non-unknowability conjecture. For all $\varphi\in\textbf{ALUT}$ and all $i\in\textbf{I}$,

Let $\gamma$ be an ordinal with Cantor normal form, and write $\alpha_1$ for its leading exponent. Let $\beta(\gamma)$ be the corresponding beta space, $sf L(\beta(\gamma))$ its logic, a…

Let ${\sf L}_3$ be the logic associated with $\beta(\omega^3)$, and let ${\sf S4.1}$ be the base logic. The Fine–Jankov formula of a finite frame is the characteristic formula used…

For each $n$, let ${\sf L}_n$ denote the logic associated with $\beta(\omega^n)$, and let ${\sf L}(\mathcal R_n)$ denote the logic of the class of $n$-roaches. n-roach conjecture.…

Let $p$ be a proposition letter, and let hspace{.2ex}\text{% tikz[baseline=-.6ex, rounded corners=.01ex, line width=.12ex] {draw (-.6ex,-.6ex) rectangle (.6ex,.6ex);}}kern.2ex and…

Let $A$ be the set of agents, and let $\KBfour+\mathbf{NE}+(\mathbf{SA_a})_{a \in A}$ be the axiom system consisting of the $KB4_n$ axioms together with the non-emptiness axiom…

Let $\widetilde{\mathfrak{G}_1^{\bullet}}$ be the frame whose validity on the closed fragment $\mathcal{F}_1$ characterizes provability in ${\mathrm{PRA}}$, and let…

Let ${\bf K^W}$ be the logic considered in the paper, let a filter be a neighborhood frame whose neighborhood collections satisfy the filter conditions defined in the surrounding d…

Let $n$ be finite, and let ${\operatorname{ILog}}(\omega^n,\preceq)$ denote the intermediate logic of the frame $(\omega^n,\preceq)$. Local finiteness claim. For all finite $n$, ……

Let $\Delta$, $\nabla$, $\bullet$, and $\circ$ denote the contingency, accident, and their dual modal operators in the bimodal logic under consideration. For $m\in\mathbb{N}$, let…

Intermediate-extension conjecture. There is a proper normal extension $\mathbf{L}$ of $\mathbf{E}$ such that

Separation property for $\mathbf{E}$. Any formula derivable in $\mathbf{E}$ is also derivable using only the axioms in group $(\mathbf{i})$ and those groups among $(\mathbf{c})$–…

Expressivity hierarchy conjecture. For all $n\in\mathbb{N}$, $\mathcal{L}_{\Rrightarrow^{n+1}}$ is more expressive than $\mathcal{L}_{\Rrightarrow^n}$.

Let $\mathfrak F$ be a class of ${\textup{\textbf{IL}}}$-frames, and define … Let $\mathfrak{All}$ be the class of frames in which every $S$-relation implication that follows both…

Let $\mathcal{DTL}^\ast$ be the dynamic topological logic with infinitary temporal modalities, and let $\mathsf L^\ast_{\Diamond f [f]\forall}$ be its monadic language with a unive…