Using Mathematical and Scientific Markup as an Approach to Model Specification
Abstract
Complex systems need to be modeled in a way that supports validation, flexible composition of component models and component model re-use. A methodology that supports these requirements must: support conceptual modeling, i.e., mathematical description, and; document the semantics embodied in a model. The expression of mathematical semantics alone will not suffice. For physics-based models, the semantics must also identify those physical laws that were applied by the modeler. Only in this way can one adequately document the particular modeling decisions made in the model's construction. The development of Markup Languages has enabled the Semantic Web, with the universal document type being expressed in the Extensible Markup Language (XML). Higher level semantic layers may be defined in XML applications such as is done with the Mathematical Markup Language (MathML). The mathematical semantics embodied within Content MathML are currently being expanded beyond the expression of "grade school mathematics" to enable the expression of higher level mathematics by the use of content dictionaries. These mathematical content dictionaries contain the definitions of semantic XML tags so that the use of well-defined mathematical concepts in a document may be unambiguously expressed by application of these tags. Building on top of this base, scientific markup languages are beginning to be developed. In particular, we have identified several requirements and some solutions towards the development of a physics markup language. For example, it must be embedded within a documentation standard that supports an accompanying natural language description. The physics markup language itself must have the ability to support the expression of physical models. This includes the concepts of: physical objects, or physical bodies, which have physical observables as properties; and physical laws, which when applied to physical objects results in model equations, or other relations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 2008
- Accession Number
- ADA638194
Entities
People
- Joseph B. Collins
Organizations
- United States Naval Research Laboratory