Emergent Mind
The Finite Model Property of Quasi-transitive Modal Logic
(1802.09240)
Published Feb 26, 2018
in
cs.LO
Abstract
The finite model property of quasi-transitive modal logic $\mathsf{K}23=\mathsf{K}\oplus \Box\Box p\rightarrow \Box\Box\Box p$ is established. This modal logic is conservatively extended to the tense logic $\mathsf{Kt}23$. We present a Gentzen sequent calculus $\mathsf{G}$ for $\mathsf{Kt}23$. The sequent calculus $\mathsf{G}$ has the finite algebra property by a finite syntactic construction. It follows that $\mathsf{Kt}23$ and $\mathsf{K}_23$ have the finite model property.
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