Abstract. In the last decade, there have been several fundamental advances in the field of ontological and linguistic metamodelling. They the use of megamodels to link abstract, digital and physical systems with a particular set of useful relations; the distinction between ontological and linguistic layers, identification and separation of them; even formalised the act of modelling and the sense and denotation of a language. In this paper, we propose second order intensions and extensions to more closely model linguistical and ontological conformance and mapping. 1 Formal modelling of languages In the classic theory of formal languages, a language L is defined as a set of sequences of alphabet symbols: L ⊆ Σ∗ [9]. This definition is easily applicable to textual languages (traditionally associated with programming) and visual languages (traditionally associated with modelling). It is also almost trivially generalisable to graph languages by substituting the reflexive transitiv...