Lately, I have been involved in an immensely challenging and interesting project: building a grammar of rituals. This post is a series of thoughts I presented to my collaborators in this project. I figure they may be of (slightly) wider interest.

I think we have to reflect on how much we need to know about the functions of a ritual, and of each ritual action, in order to build something like a grammar.
Grammar has categories and mechanisms only because it needs to express many things with a limited set of components; if we have no idea of what it attempts to express, or why its inventory is limited, it seems impossible to find and make sense of the rules.
We can do superficial pattern-matching, but without knowing what the patterns signify and how they relate, the probability of finding the right parsing is ridiculously small (take e.g. genomics, which has infinitely more data than us, the support of chemistry and developmental experiments to test its hypotheses, and probably more papers/year than all humanities put together, and is still stuck on some fundamental definitional problems).

So, although it is not our purpose to come up with another grand theory of what rituals mean, we do need minimal hypotheses on what their rules are meant to encode. Once we discard every attitude on myth that is incompatible with intrinsic grammaticality (e.g. myth dramatization, as a script or template is not a grammar), it seems that anthropologists believe ritual actions are about establishing ties between different entities, and using these ties to move some of them across the bounds of their categories. I am hoping that I will learn soon if a mimamsaka would agree with that basic notion.

Chapter 5 of McClymond deals with the apportionment phase of ritual (dividing the offering, and instructions for acting upon the parts or giving them to certain participants). Like many others, she connects it to the analogical mode of thinking: each part of the offering is made to correspond to a part of the cosmos, and to a part of society, and so on, though it is often unclear why something is made to correspond with something else.

Descola argues that this (common but not universal) mode of thinking is rooted in an essentially dissociative worldview: each object is a singularity, made of singularities, and while resemblances can be found and categories drawn, they essentially unstable and open to negotiation. This negotiation proceeds by small increments, passing from neighbor to neighbor, because there are no "highways" of absolute ordering (e.g. even a yin object can be divided into equal yang and yin parts, there is no conservation of yin-ness). Each classification is not the but an ordering of the world, built poetically or pragmatically, and abundant contradictions are not a sign of irrationality or inconsistency. Levi-Strauss argues that, when associations are made, they are not associations of objects, but of contrasts between objects, which are more stable than the former.
Let's believe all that, for now.

Clearly and crucially, we are not analogists: our culture has seen a triumph of philosophical materialism, which provides stable relationships between objects. There is no need to establish a tie if physical laws already provide it (e.g. X and Y are substitutable because they have the same substance), and if they don't, there is nothing we can do - the tie is only imaginary. Thus, at most, the intuitions of analogism can arise for us when we consider mental states, and possibly social states (those are still sufficiently "in the mind"), but not entities and essences. God does not play word association with the universe.

If we believe in this cultural shift, it should natural for us to think of the semantics of ritual as, for instance, a fluid mechanics or energetics of impurity, sacrality or some such affective/religious attribute - but this is perhaps not how they would have been perceived. We think in terms of communicating vessels and prices paid - conservation and conversion - and other abstract ordering principles. They were certainly available as analogies, but I don't think any of them would have been taken as universal or inviolable, and placed at the heart of every ritual in every culture. Though I can easily conceive that such principle would be consciously established as part of ritual science, as a reliable technique, rather than a property inherent to what is being manipulated.

So, putting all the threads together: under the hypothesis of grammaticality, every ritual action worth memorizing and transmitting, although it may not always have an overt meaning in itself (like grammatical words), should contribute alone or in combination to the expressive power of the sequence. Grammaticality allows repetition and ornament (e.g. for emphasis) but never redundancy; strictly useless or equivalent terms are always unstable.
Under the hypothesis that ritual operates in the sphere of analogy, what is being expressed is a certain mapping between entities, and a negotiation of their categoric status. Part of that meaning is provided by semantic associations for a given act; these are "lexical" semantics, possibly arbitrary and beyond explanation (except e.g. by "etymology" or external referents such as myth or cooking).
But a whole fraction of the semantics is embedded in the grammar: those are "casual" semantics, the meaning (i.e. analogical expressive power) of ritual categories and rules. This is what we probably need to posit or uncover as we investigate rituals, and before we delve into pattern-matching. Of course, each ritual language may have its own "case system"; but hopefully, there will be common features, the likes of adjunction, determination, predication, and so on.
Though it would be enough for a start to find something that is not universal but very common and strikingly grammatical, e.g. active/passive.

Descola, Philippe. Beyond nature and culture. University of Chicago Press, 2013.
Lévi-Strauss, Claude. La pensée sauvage. Plon, 1962.
McClymond, Kathryn. Beyond Sacred Violence: A Comparative Study of Sacrifice. JHU Press, 2008.