The Bernays–Schönfinkel class (also known as Bernays–Schönfinkel-Ramsey class) of formulas, named after Paul Bernays

Paul Bernays

Paul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...

 and Moses Schönfinkel

Moses Schönfinkel

Moses Ilyich Schönfinkel, also known as Moisei Isai'evich Sheinfinkel , was a Russian logician and mathematician, known for the invention of combinatory logic.- Life :Schönfinkel attended the Novorossiysk University of Odessa, studying mathematics under Samuil Osipovich...

 (and Frank P. Ramsey

Frank P. Ramsey

Frank Plumpton Ramsey was a British mathematician who, in addition to mathematics, made significant and precocious contributions in philosophy and economics before his death at the age of 26...

), is a decidable fragment of first-order logic

First-order logic

First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

 formulas.

It is the set of satisfiable formulas which, when written in prenex normal form

Prenex normal form

A formula of the predicate calculus is in prenex normal form if it is written as a string of quantifiers followed by a quantifier-free part .Every formula in classical logic is equivalent to a formula in prenex normal form...

, have an quantifier prefix and do not contain any function symbols.

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.