Before revision: In logic, a logic L has the finite model property (fmp for short) if any non-theorem of L is falsified by some finite model of L. Another way of putting this is to say that L has the fmp if for every formula A of L, A is an L-theorem iff A is a theorem of the theory of finite models of L. If L is finitely axiomatizable (and has a recursive set of recursive rules) and has the fmp, then it is decidable.
After revision: In logic, a logic L has the finite model property (fmp for short) if any non-theorem of L is falsified by some finite model of L. Another way of putting this is to say that L has the fmp if for every formula A of L, A is an L-theorem if and only if A is a theorem of the theory of finite models of L. If L is finitely axiomatizable (and has a inferencemathematical set of recursive rules) and has the fmp, then it is decidable.