The Bernays–Schönfinkel class (also known as Bernays–Schönfinkel–Ramsey class) of formulas, named after Paul Bernays, Moses Schönfinkel and Frank P. Ramsey, is a fragment of first-order logic formulas where satisfiability is decidable.
It is the set of sentences that, when written in prenex normal form, have an
is a formula in the Bernays–Schönfinkel class with one free variable, then either
[1] This class of logic formulas is also sometimes referred as effectively propositional (EPR) since it can be effectively translated into propositional logic formulas by a process of grounding or instantiation.
[2] Efficient algorithms for deciding satisfiability of EPR have been integrated into SMT solvers.