In this work we illustrate how the mathematics of rational thinking is formally equivalent to that of structural mechanics. Concepts from the wold of logic, such as accuracy, uncertainty, Maximum a Posteriori (MAP) and rationality correspond, in the world of mechanics, to stiffness, flexibility, equilibrium and conservativeness. For instance, a linear Gaussian N-parameter estimation problem can be solved through a N-dof linear elastic system, as the analogy goes along these lines: the parameters covariance matrix is the system's flexibility matrixthe Fishers information is the stiffness matrixthe negative log-distribution of the parameters is the elastic potential energy of the systemthe Maximum a Posteriori (MAP) is the state of static equilibrium. In principle, based on this analogy, we could reproduce any logical inference problem with a finite element model, and make a judgment by finding its equilibrium state. We will show application of this analogy to a number of civil engineering inference problems, including Bayesian estimation, Bayesian networks and Kalman filter
