It is explored how foundational ontologies based on physicalist materialism, nominalism, and Peircean semiotics can be applied to represent signs, models of physical systems, and their use in engineering modelling and simulation practice. It is argued that to conceptualize modelling of physical systems in such a framework, various kinds of Peircean semiotic triads need to be combined. Thereby, a sign (representamen) and a represented object either yield an interpretant, i.e., another representamen of the same object, or the representation is transferred to another object by semantic change through metonymization or metaphorization, retaining the same symbol. Multiple conceivable ways of implementing this ontological paradigm are compared, and a demonstrator implementation is discussed.