As the title indicates, this chapter contains a comprehensive survey of multi-valued algebras that have been proposed for hazard detection. Of perhaps as much value as a study of the properties that enable hazard detection is the complete characterization of each algebra, and a determination of its place in a very complete hierarchy of algebraic structures that range from semi-groups through semilattices, lattices, Demorgan algebras, Boolean algebras, and ternary algebras. Independent of hazard analysis, I found the review of algebraic properties of each structure in the hierarchy very instructive. Therefore, I recommend this chapter not only as required reading for anyone interested in hazard detection, but also to anyone interested in discrete mathematical modeling, regardless of the application.

After introducing an infinite algebra, C, the authors show how almost all of the algebras commonly used for hazard detection can be derived either as finite quotient algebras of C relative to congruence relations on C; as subdirect products (cross-products) of the quotient algebras with each other, with Boolean algebras, or with ternary algebras; or as augmented algebras based on adding additional elements to the algebras just described. Again, this analysis is of great interest from a purely mathematical point of view, and undoubtedly has applications beyond hazard detection. This chapter would be appropriate for use in a class in algebraic structures.

This chapter is also one of the most complete surveys of hazard detection by simulation using algebraic approaches that currently exists. It is definitely worth reading.