Skolemization and Decidability of the Bernays-Schoenfinkel Class in Goedel Logics
Authors
Mariami Gamsakhurdia
Matthias Baaz
Anela Lolic
Abstract
In 1928, Bernays and Schoenfinkel proved the decidability of prenex sentences whose matrices contain no function symbols, now known as the Bernays-Schoenfinkel (BS) class. We investigate the decidability of the BS class for all Goedel logics. Our validity argument relies on the fact that Skolemization works for prenex Goedel logics, while 1-satisfiability follows from structural properties of prenex formulas. We show that validity and 1-satisfiability for the BS class are decidable in every Goedel logic, and that these properties persist across all infinite Goedel logics.
