Remember the objective of the dialectic is to develop, improve and transform ideas, thinking, arguments and situations by doing the three senses. The objective of the propositional is to validate ideas, arguments and explanations (theories) by invalidating, if the/an alternative, contradictory, ideas, explanations, thinking and argument cannot be falsified by the examined then the examined is invalid/ated.
Look at the difference in searching for ways forward and development and how to do it. The propositional does not allow contradictions whilst the dialectical draws on them.
And thus
the dialectic can include the propositional, but the propositional cannot include the dialectical and must reject and invalidate to exist as a valid construct
From my conference presentation at the Association of Educational Development in Africa - 14th of April in Cape Town
Testing Transformation through Dialectics
Edited by Alon Serper
AEON-ESSRI (NMMU) Ethics Hub
Earth Stewardship Science Research Institute
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Serper, A. (Ed.). (2015). Testing Transformation through Dialectics. Trébol Press, Los Angeles, USA (www.trebolpress.com), possibly in collaboration with Unisa Press, RSA (http://unisa.ac.za)