84 problems

Let the logic of Section $\mathrm{logics}$ be the logic studied in the paper, and let its completeness proof be the proof given in the appendix. Consider more expressive languages…

The paper considers a quantifier-free term modal logic without function symbols, augmented with the basic assignment modalities from dynamic logic. Decidability conjecture. This fr…

A topological model consists of a topological space together with the valuation of proposition letters and nominals; let $T_2$ denote the class of Hausdorff spaces, and let…

Let ${\bf GL}$ be Gödel–Löb provability logic, let … and define Solovay's logic by … Let ${\bf S5}$ denote the modal logic of equivalence frames, and let $\rightthreetimes$ denote…

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…

Expanding commutator conjecture. Setting $\mathsf{L}_v\in\{\mathsf{K4},\mathsf{K4.3}\}$ should lead to incompleteness, whereas setting…

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…

Extension conjecture. Many of the complexity results proved for ${{\mathrm{PL}}\xspace(\normalfont\textsc{ne})}\xspace$ should extend naturally to other convex union-closed logics,…

The paper considers the logics of matches and the formulas listed in Proposition … provide complete axiomatizations of the logics of matches. The preceding discussion establishes i…

Buttons are modal assertions that, once made true, remain true in all further extensions. Hamkins and the authors' buttons-suffice conjecture. The existence of buttons suffices to…

Conjecture on the axiom T. The rewriting rule for this axiom should be defined by duplicating the tree and attaching the copy as a fresh child.

Crisp-frame characterization conjecture. The principle $--\Diamond x \rightharpoonup \Diamond --x=\top$ characterizes crisp frames.

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…

For each of the intuitionistic modal logics $\mathbf{L}_{\mathbf{bc}}$, $\mathbf{L}_{\mathbf{dc}}$, $\mathbf{L}_{\mathbf{bdc}}$, $\mathbf{L}_{\mathbf{fbdc}}$,…

Let $\mathbf{L}_{\min}$ be the minimal intuitionistic modal logic, and let $\mathtt{Log}(\mathcal C_{\mathbf{uc}})$ and $\mathtt{Log}(\mathcal C_{\mathbf{quc}})$ denote the logics…

Goldblatt–Thomason conjecture for distribution-free modal logics. The classical Goldblatt–Thomason theorem should lift to the sorted modal logic case, yielding a related result for…

A unimodal logic is prelocally tabular when it has a locally tabular extension. Consider logics above ${\textsc{S4}}\times {\textsc{S5}}$, meaning extensions of this product logic.…

Let B-eS denote the paper's base-extension semantics, and let validity in B-eS, validity in the Kripke semantics, and the stated theorem be understood as in the paper. Inverse-vali…

Complexity conjecture. The construction given in Theorem $$ leads to a $\mathrm{PSpace}$ upper bound for all $m$.

Let $L$ be a modal logic, and let a descriptive frame and a Kripke frame for $L$ have their usual meanings. Say that $L$ is strongly Kripke complete when every $L$-consistent set o…

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

Completeness conjecture. The completeness of non-classical variants of $\mathsf{S4}$ may be proved by combining the methods of Balbiani et al. and Baltag et al.