Semiotic theory of American philosopher and mathematician C.S. Peirce elaborates philosophy of index according to reference here:
Peirce argued that logic is the formal study of signs in the broadest sense, not only signs that are artificial, linguistic, or symbolic, but also signs that are semblances or are indexical such as reactions. Peirce held that "all this universe is perfused with signs, if it is not composed exclusively of signs", along with their representational and inferential relations. He argued that, since all thought takes time, all thought is in signs: To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs.
An index is a sign that denotes its object by virtue of an actual connection involving them, one that he also calls a real relation in virtue of its being irrespective of interpretation. It is in any case a relation which is in fact, in contrast to the icon, which has only a ground for denotation of its object, and in contrast to the symbol, which denotes by an interpretive habit or law... If an indexical relation is a resistance or reaction physically or causally connecting an index to its object, then the index is a reagent (for example smoke coming from a building is a reagent index of fire). Such an index is really affected or modified by the object, and is the only kind of index which can be used in order to ascertain facts about its object. Peirce also usually held that an index does not have to be an actual individual fact or thing, but can be a general; a disease symptom is general, its occurrence singular; and he usually considered a designation to be an index, e.g., a pronoun, a proper name, a label on a diagram, etc.
So in semiotics a reagent index is not denoting any object as icons or interpretive symbols by some habit, but denoting a real relation (connection) involving a certain object with other objects. So in this sense reagent index corresponds to ontic causality and symbols and icons have nothing to do with causality. Unlike various conditionals connectives used in logic, indexes are heavily used in set theory, (Saussurean) linguistics and computer programming languages to express the idea of (causal) relation or mapping between domain objects or categories.