Systemigrams are visual representation of overall architecture of a system. Systemigrams are used to understand and model a system. What are the syntax and semantics of systemigrams?
to me, they look like basic entity-relationship diagrams - I'm not really sure why they merit their own name. AFAIKT, the syntax is a directed graph with nouns/entities as vertices, and relations/verbs as edges. semantics, well, semantics is in the eye of the beholder...
If you need an architecture modeling language for describing the construction and operation of business processes, organizational structures, information flows, IT systems, and technical infrastructure may be ArchiMate suits you more:
Systemigrams are arbitrary influence diagrams designed with SystemiTool, a non-open source application. They offer a way to visualize a system, but are highly user dependent. In other words, if you had 20 stakeholders design a systemigram of a system, you would likely get around 30 different visualizations. Therefore, its optimal use is for visualizing stakeholder perspective.
As a systems analysis tool, Systemigrams do not provide an improvement over classic influence diagrams; depend heavily on the Jay Forrester school of system dynamics (whose adherents like to refer to it as "systems thinking," a bastardization of Russell Ackoff's use of the term); and, as noted, are not an open-source application so the benefit is to those selling licenses. Systemigrams are promoted as system visualization tools as they do not provide workable models of dynamic systems that could be used in an analysis of alternative solutions. They basically provide a pretty picture.
A system analyst has many more useful tools available depending on the nature of the system. Bayesian belief networks, Ishikawa diagrams, Petri Nets and, if the five-sided wind tunnel is sponsoring your work, SysML.
Entity relationship diagrams are only suitable for describing pure data.
Systemigrams are used to describe the system, so it is best that their syntax and semantics are able to describe structure and behavior in an integrated manner.