 As we have seen, a new modality can be introduced in syntactic terms (using the language to provide a formula defining the new concept), but also in a semantic way (using the semantic counterparts of the existing modalities to define a further semantic notion, which in turn is used to interpret the new modality). Our examples so far have been restricted to the use of one of these two strategies, but their interplay is also possible. The case to be discussed here concerns the  plausibility models  of Board (2004); Baltag and Smets (2006, 2008); van Benthem (2007); here, the presentation of Baltag and Smets (2008) is used.