We have created a logic-based, Turing-complete language for stochastic modeling. Since the inference scheme for this language is based on a variant of Pearl's loopy belief propagation algorithm, we call it Loopy Logic. Traditional Bayesian networks have limited expressive power, basically constrained to finite domains as in the propositional calculus. Our language contains variables that can capture general classes of situations, events and relationships. A first-order language is also able to reason about potentially infinite classes and situations using constructs such as hidden Markov models(HMMs). Our language uses an Expectation-Maximization (EM) type learning of parameters. This has a natural fit with the Loopy Belief Propagation used for inference since both can be viewed as iterative message passing algorithms. We present the syntax and theoretical foundations for our Loopy Logic language. We then demonstrate three examples of stochastic modeling and diagnosis that explore the representational power of the language. A mechanical fault detection example displays how Loopy Logic can model time-series processes using an HMM variant. A digital circuit example exhibits the probabilistic modeling capabilities, and finally, a parameter fitting example demonstrates the power for learning unknown stochastic values.

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Critical infrastructure and its interdependencies play a vital role in our daily functions. Our economies, government, and way of life depend on the sound function of these integrated systems. Analysis of these systems, however, has historically been limited: system owners and operators have limited information outside their domain space (and that legal impediments often limit their ability to better understand the broader system), and very few entities have the desire to better understand these systems as a whole, let alone their interconnections. The National Infrastructure Simulation and Analysis Center (NISAC) is one such entity. NISAC, a program managed by the U.S. Department of Homeland Security (DHS) and comprised of a core partnership of Sandia National Laboratories (SNL) and Los Alamos National Laboratory (LANL), draws on years of modeling experience of various types, focused on infrastructure, population, and the economy, to examine questions pertinent to DHS regarding the function of economy and critical infrastructure of the United States (see Figure 1).

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