The original purpose of the C standard was to solve the problems created by the diversity of increasingly divergent implementations of C. They studied existing behavior across systems, proposed new language constructs, and it was generally a success (look at the proliferation of C in the 90s across many different systems and architectures).
The actual informal semantics in the standard and its successors is written in an axiomatic (as opposed to operational or denotational) style, and is subject to the usual problem of axiomatic semantics: one rule you forgot to read can completely change the meaning of the other rules you did read. There are a number of areas known to be ill-specified in the standard, with the worst probably being the implications of the typed memory model. There have since been formalized semantics of C, which are generally less general than the informal version in the standard and make some additional assumptions.
C++ tried to follow the same model, but C++ is orders of magnitude more complex than C and thus the standard is overall less well specified than the C++ standard (e.g. there is still no normative list of all the undefined behavior in C++). It is likely practically impossible to write a formal specification for C++. Still, essentially all of the work on memory models for low-level programming languages originates in the context of C++ (and then ported back to C and Rust).
