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Tableau-based translation from first-order logic to modal logic

Perkov Tin, Mikec Luka

Reports on Mathematical Logic

2021

Vol. 56

57--74

We define a procedure for translating a given first-order formula to an equivalent modal formula, if one exists, by using tableau-based bisimulation invariance test. A previously developed tableau procedure tests bisimulation invariance of a given first-order formula, and therefore tests whether that formula is equivalent to the standard translation of some modal formula. Using a closed tableau as the starting point, we show how an equivalent modal formula can be effectively obtained.