Resolution and the Decision Problem

Abstract

The decision problem (or the “Entscheidungsproblem”) of first-order logic can be traced back to the early years of the 20th century. Around 1920 Hilbert formulated the problem to find an algorithm which decides the validity of formulas in first-order predicate logic (see, e.g., [11]). He called this decision problem the “fundamental problem of mathematical logic”. Indeed, in some informal sense, the problem is even older than modem symbolic logic. G. W. Leibniz already formulated the vision of a calculus ratiocinator [16], which would allow to settle arbitrary problems by purely mechanical computation, once they had been translated into an adequate formalism.