This has been discussed on the RO discussion list. What follows is a summary of the results of the discussion.
The RO epistemic relationship definitions are strongly informed by David Schum's work, particularly "Thoughts about a science of evidence" ( http://www.evidencescience.org/content/Science.doc\) and Anderson, T., Schum, D., Twining, W. Analysis of Evidence, 2nd ed. Cambridge University Press, 2005
All epistemic relations are meta-level instance relationships. That is, they relate evidence to a proposition. They are therefore expressible only in OWL Full. Epistemic relations cannot be modeled as an owl:AnnotationProperty because one cannot define subproperties or domain/range constraints for annotation properties.
The top-level epistemic relationship is called "is_relevant_to" (along with its inverse, "has_evidence"). It relates evidence to a proposition. Evidence is an instance of an OBI:DENRIE (that is, an information entity that is either a collection of bits that can be interpreted by a computer or a dependent_continuant which conveys meaning and can be documented and communicated -- see https://wiki.cbil.upenn.edu/obiwiki/index.php/DigitalEntityTerms\). A proposition is a statement that can be either true or false. OBO propositions are OWL individual axioms (http://www.w3.org/TR/owl-ref/#Individual) whose class membership and property values are drawn from OBO ontologies. OBO propositions, so defined, may be coextensive with OBI:Hypothesis, which is not yet well defined.
IS_RELEVANT_TO / HAS_EVIDENCE
Evidence E RO_proposed:is_relevant_to proposition P iff E can be linked by inference to P. (See "Analysis of Evidence," 2nd edition, pp. 76-77) The OWL:inverse_of relationship is P RO_proposed:has_evidence E
SUPPORTS / IS_SUPPORTED_BY
Evidence E RO_proposed:supports proposition P iff E can be linked by inference to establishing that P is true. The OWL:inverse_of relationship is P RO_proposed:is_supported_by E.
CONTRADICTS / IS_CONTRADICTED_BY
Evidence E RO_proposed:contradicts proposition P iff E can be linked by inference to establishing that P is false. The inverse relationship is P RO_proposed:is_contradicted_by E.
Supports and contradicts relations are related to each other via negation of the proposition. Negation (and the term "not") are part of owl, so the following is not expressed in owl:
E supports P is-equivalent-to E contradicts (not P)
E contradicts P is-equivalent-to E supports (not P)
It is not clear if there is a need for analogous class-level relations; all OBO relations among universals are defined to be true (under all-some quantification). If class-level epistemic relations are necessary, their definition based on the instance-level relationships above is straightforward.