Unification in subsystem J$_2$ of provability logic GLB

Abstract

We generalize methods, developed by S. Ghilardi, and apply them to a subsystem J$_2$ of bimodal provability logic GLB. We describe projective formulas in J$_2$ in terms of Kripke semantics and prove that logic J$_2$ has finitary unification type. As an application, we show that admissibility problem for J$_2$ is decidable.

Figures (4)

• Figure 1: шкалы Игнатьева
• Figure 2: $\mathbf{J}_2$-шкалы
• Figure 3: (\ref{['condition_stratif']})
• Figure 4: стратифицированные модели

Theorems & Definitions (13)

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