I am analyzing a pro-Israel speech by Mark Pence in which he announces that America stands with Israel. I am using presuppositions as a tool of analysis but don't know under which tenet of CDA the scope of my paper would fall.
Certainly. By choosing the related news corpora on America's support for Israel, you can use a relevant CDA model to reveal the politicians' partisanship towards Israel.
As you know, according to CDA, language is a form of social practice. From this perspective, you can describe, interpret, analyze, or critique social and political life reflected in text by using critical discourse analysis (CDA). For the application of CDA specific research methodology in the analysis of political discourse, especially at the level of international relations, I recommend:
Methods of Critical Discourse Analysis edited by Ruth Wodak & Michael Meyer (2001).
Chilton, P. and C. Schäffner (2002). Introduction: Themes and Principles in the Analysis of Political Discourse. In P. Chilton and C. Schäffner (eds.), Politics as Text and Talk. Approaches to Political Discourse. 1–41.Amsterdam: John Benjamins.
CDA should rather be seen as an approach, position or stance of studying text and talk, as stated by Teun van Dijk (1995). You can therefore use Teun van Dijk's socio-cognitive perspective, starting from the idea that the presupposition works as a discursive condition through which power prefigures certain meanings and representations:
van Dijk, T. A. (1995). Aims of Critical Discourse Analysis. Japanese Discourse, 1 (1): 17-27.
But I also recommend Norman Fairclough's dialectical-relational perspective:
Fairclough, N. (1995). Critical Discourse Analysis. London: Longman.