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This paper applies operads and functorial semantics to address the problem of failure diagnosis in complex systems. We start with a concrete example, developing a hierarchical interaction model for the Length Scale Interferometer, a high-precision measurement system operated by the US National Institute of Standards and Technology. The model is expressed in terms of combinatorial/diagrammatic structures called port-graphs, and we explain how to extract an operad LSI from a collection of these diagrams. Next we show how functors to the operad of probabilities organize and constrain the relative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive forward and back
Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe ModelingTo
A pairing function J associates a unique natural number z to any two natural numbers x,y such that for two unpairing functions K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold. Using pairing functions on natural number represe
Multi-relational networks are used extensively to structure knowledge. Perhaps the most popular instance, due to the widespread adoption of the Semantic Web, is the Resource Description Framework (RDF). One of the primary purposes of a knowledge netw
The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Fruhwirth, we consider an extension of this theory with an additional predicate for fi