Semantic web services present a new challenge in distributed knowledge integration. Under the Simple Semantic Web Architecture and Protocol (SSWAP, http://sswap.info), web resources publish information about their data and services in terms of OWL ontologies. With semantic tagging, the output of one service can drive the input of another, presenting the alluring prospect of machines autonomously assessing the suitability of web resources for distributed workflows. Ontological reasoning under OWL greatly expands the potential for semantic web service interoperability by guaranteeing the compatibility of resources using such techniques as inferencing, typing, and class subsumption. Formal methods for managing such structures are urgently needed. Recent advances in the mathematics of hierarchies can formalize the construction of synthetic hierarchies from unstructured information, identifying mutual subsumption architectures. Here we examine the problem space and describe the promise of mathematical order theory (formal concept analysis and lattice metrics) for advancing knowledge integration in open worlds.