Given the vagueness of those terms and the overlapping aspects of what is subsumed under them, I think the only effective tool at present is the brain.
I don't want to engage in the theoretical discussion whether it is possible or not, but we tried to do this in an article about the innovation paradigm. YOu can have a loot at the paper, even if you are not interested in innovation, because it provides also information about the way we operationalized paradigms based on axiological, ontological and epistemological dimensions. I guess you will find useful information in the attachment
The question rather begs the question of what are the ontological, epistemological and axiological assumptions of an approach that seeks tools in order to approach its questions (eg by looking for a tool don't you create the object of inquiry As an object?). How reflexive is your tool-led approach? Of what community of practice does use of such analytic tools make you a member?
There is no single tool. I think that there is a set of data to be evaluated that do not fit the same evaluation - epistemology cannot be treated in the exactly same way as axiology - it is necessary to consider the specifics of each situation.
But you'll find a basis int this paper => Conference Paper ONTOLOGY, EPISTEMOLOGY AND AXIOLOGY IN QUANTITATIVE AND QUAL...
"It is clear that if the brain sciences do not want to degenerate into a physics or chemistry of living—or having once lived—tissue they must develop a theory of the brain: T(B). But, of course, this theory must be written by a brain: B(T). This means that this theory must be constructed so as to write itself T(B(T))." (Heinz von Foerster, Understanding Understanding, p. 195).
Or, in other words, as soon as things start to get reflexive (as in cybernetics), the ontological, epistemological, and axiological get entangled with each other. In the OP, it is the evaluator of the researchers needs to examine *themselves* in these terms.
It would seem that a question like this would likely be most relevant in qualitative research, as this is the form of research in which such issues as the researcher’s philosophical predispositions play the greatest role in generating the findings (quantitative research, on the other hand, attempts to use statistical data gathering in order to avoid allowing the researcher’s presuppositions to taint the findings.) In general, in qualitative research, how such presuppositions are made clear is that the researcher will simply lay them out explicitly so that readers will be aware of the kinds of philosophical assumptions the researcher will make. Thus, we may be able to come up with a few measures, but the question then becomes how will they be used? Qualitative research assumes that one’s presuppositions are consciously accessible, and so a “measure” wouldn’t quite be necessary, and quantitative research attempts to avoid allowing presuppositions to come into play during data analysis. I think that before we start developing measures, we always need to think first about how they might be useful.
If you would like to make a comment in this and give your opinion on how such measures as the OP is talking about may be useful, please feel free to do so and mention me—I am curious to see what everyone thinks.
Perhaps - depending on what it is that you want to evaluate. Let's say that each of those (ontology, epistemology, axiology) may each be represented by a set of statements or propositions. You could certainly look at that set of propositions and compare them with other sets of propositions and simply calculate the number of concepts that the two sets have in common. This could let you quantify the extent to which two views have in common. Alternatively, you might use Integrative Propositional Analysis (IPA) to evaluate the causal logic structure of each set of propositions to determine the extent to which each might be useful (at least, from a structural perspective). We do this a lot with theoretical models and similar sets of propositions. it might work well with yours too. For some resources, see my publications or: https://projectfast.org/resources-for-researchers/
It always depends on the perspective of your domain. On the other hand, it is very difficult to assert any tool because the notion is always subjective. But yes.....there are lots of tool in Indian philosophical systems because they have fixed motive that is self-realisation or liberation. according to their systems, they have chronologies.
There is no particular perspective, because philosophical analysis rebels against framing!. Perhaps a good way to address these main philosophical questions is for the researcher to get to know the nature of each question and how he can ask an ontological , an epistemological, and an axiological question within the context of his topic.