The "causal models framework" analyzes counterfactuals in terms of systems of structural equations. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence ""Y" would be "y" had "X" been "x"" (formally, "X = x" > "Y = y" ) is defined as the assertion: If we replace the equation currently determining "X" with a constant "X = x", and solve the set of equations for variable "Y", the solution obtained will be "Y = y". This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by Judea Pearl (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.