In principle, a theory of signs admits that anything can be used to describe anything else. In practice, there are severe limitations on the use of some entity as interpretant of another, and these limitations derive from the cultural and local context, from the symbolic system used, and from the cognitive and ontological underlying motivations. This is a theory which only describes the use of signs as a post-hoc issue, after some intentionality has decided what is an interpretant of what. Interpretant is a relation which holds between any two entities, where the first is used to describe or explain the second. There are background conditions for being an interpretant: an agent should be aware of both the interpretant and the reference, and a context should encompass the agent and the entities involved. Interpretant is reflexive, while symmetry and transitivity are debatable. Symmetry seems inappropriate, since usually some entity is USED as interpretant, and the process is not reverted (not an equivalence). Transitivity holds only if metaphor and metonymy are discarded as possible sense sources in the domain of interpretation.
(=> (Interpretant-Of ?A ?B)
(And (_Intentional ?A True)
(Exists (?Z ?W)
(And (Situation ?Z)
(*Agent ?W)
(Context-Of ?Z ?W)
(Context-Of ?Z ?A)
(Context-Of ?Z ?B)
(Aware-Of ?W ?A)
(Aware-Of ?W ?B)))))