The official standard for conceptual graph syntax and semantics is the ISO/IEC 24707 standard for Common Logic, which defines the semantics in terms of an abstract syntax and model-theoretic semantics. To download a copy of the standard (free for personal use), see
http://standards.iso.org/ittf/PubliclyAvailableStandards/c039175_ISO_IEC_24707_2007(E).zipAnnex B of this document defines a grammar for the Conceptual Graph Interchange Format (CGIF) and defines its semantics by a translation to the abstract syntax of Common Logic. The old draft ANSI standard for conceptual graphs is obsolete.
However, the rules for CGIF published in Annex B of that document are complex because they combine both the CGIF syntax and the translation to the CL abstract syntax in the same rules. That makes them look more complex. For a short summary that extracts just the CGIF grammar rules, see
The official ISO standard is not a good place to start for anybody who wants a quick introduction to CGs. For a convenient introduction with examples and discussion, see