The semantics of a set of CML top level forms is provided by translating them into first order logic such as defined in KIF. CML inherits the logic's model-theoretic semantics. Fully formalizing CML requires two steps:
, page , defines the
translation from each top level form into logic. This is done by
defining the syntax of each form and then providing an axiom schema
that maps the syntax into a set of axioms.
The underlying objects are only partially formalized.
For instance, Section , page
provides a specification of quantities, dimensions, and units.
Other aspects, such as arithmetic or standard theorems of calculus and
mathematics, are not axiomatized. All models of a CML theory must
satisfy such background theorems and all implementations are assumed
to respect them as well.
There are some difficulties associated with the use of composable
equations (See section , page ). These require a closed
world assumption, which in turn requires CML to be defined in terms of
a non-monotonic logic. This does not change the axiomatization, but
rather affects the underlying semantics, as non-monotonic logics do
not have a standard Tarskian model theory.