5 problems

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 ${\sf ILW}^*$ and ${\sf ILP}_0$ be the logics described in the paper, and let ${\sf ILP}_0{\sf W}^*$ denote their union. Write $\mathfrak{Il}({\sf all})$ for the logic valid in…

Let ${\sf ILW}$ be the interpretability logic obtained by extending interpretability logic ${\sf IL}$ with the principle ${\sf W}$, … Here $\mathfrak{Il}({\sf all})$ denotes the lo…

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 $A$ and $B$ be formulas, and let ${\textup{\textbf{IL}}{\sf{W^*P_0}}}$ and ${\textup{\textbf{IL}}({\rm All})}$ denote the corresponding interpretability logics, with…