The root of logic is based on the rationalism which investigates the cause and effect. It is guided by "positivistic" epistemology. In new paradigm research how is this logic incorporated?
I thought that a positivist/postpositivist approach was more appropriate for quantitative research. Generally cause and effect scenarios stem from quantitative research as well (Creswell, 2009).
Reference: Creswell, J. (2009). Research design: Qualitative, quantitative, and mixed methods approaches 3rd. Thousand Oaks, CA: Sage Publications.
Frilund et al. 2013. Assessment of ethical ideals and ethical manners in care of older people. In this article I have used BBN as a method for compute clusters with underlining items. The data witch was used was symbolic data, and the numbers witch was used was ordinary. The clusters and the item was namned with concepts and statements in line with the theory of Caritative caring, By using concepts and statements in line with a given theory the symbolic data move over to logical. You are welcome to read the article, may be it can help you to incorporated a logical approach and give your data mening in relation to the perspective you want to referee to.
Traditionally, qualitative research has indeed rejected naive notions of cause and effect, based on its emphasis on subjectivity, and hence the idea that cause and effect is more perceived than "real."
More recently, there has been a renewed interest pragmatism as a philosophical system, especially among those doing grounded theory. Most of that work (by people like Anthony Bryant and Kathy Charmaz) has concentrated on abduction as an alternative to the distinction between induction and deduction. In terms of connecting observations with theory, abduction poses an If...then relationship: If my theory is correct, than that would explain the things I have observed.
In general, pragmatists use action as their key to understanding. In the case of abduction, that would mean acting on the belief implied in an If...then statement to find out if the predicted consequences do occur. In the case of cause and effect, this would amount to something like: "If I believe that this cause can be linked to this effect, then I need to act on that assumption in order to observe the consequences."
Pragmatism thus rejects both the search for truth in positivism and the widespread subjectivism of much "alternative paradigm" thinking, and replaces it with an emphasis on how humans actually act and reason.
Logic is about using concepts and it's just concepts that are central in qualitative research. One challenge in qualitative research is that it have to develop new conceptual structures but it has been done in a loose way. Logic is perfect for defining conceptual hierarchies, see my article Hautamäki Antti (1992): "A Conceptual Space Approach to Semantic Networks", Computers & Mathematics with Applications 23 (1992), 6-9, March-May, s. 517-526.
Logical inference is a cental way to "expand" knowledge in qualitative research. Here one can apply not only deductive logic, but also inductive and abductive logic. Say diagnosis is based on abduction. Also so called default reasoning is relevant: say in mental frames we use default values as starting point. I feel also that conceptual space approach developed independently by me (1986) and Gärdenfors (1990, 2000 etc) is extremely useful in qualitative research. See e.g.Kaipainen Mauri ja Hautamäki Antti (2011): ”Multi-Perspective Knowledge Organization, Explorative Conceptualization of Topical Content Domains”. Knowledge Organization 38 (2011), no.6., 503-514.