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I've been trying to understand GraphQL queries (e.g. Wikidata) with Formal Concept Analysis but my first stumbling block is that most between-object relations at least in the Wikidata ontology are signed, they have a "from" and a "to".

Let me maybe rewind: an incidence structure is $(G,M,I)$ where $G$ is a set of "points" and $M$ is a set of "lines" and $I\subset G\times M$ is the incidence relation. So for example $(G,M)$ could be a bipartite graph; or $G$ could be a set of edges that are incident to nodes in a simple graph. Formal concept analysis is a theory of lattices over incidence structures where $G$ are "concepts" and $M$ are "attributes".

Google finally tells me that there are higher-order incident structures with more "types of entities" (i.e. $G_1, \cdots, G_r$ but as best as I can tell as a nongeometer, these still have a single incidence relation. And what I need is something like $(G,M,I\times \sigma)$ where $\sigma=\{-1,1\}$ is the sign or orientation of the incidence relation.

My question is "does this exist as something with an already-existing literature"? I do know that directed graphs in network flow problems can be represented as signed incidence matrices, but I'm trying to see if I can minimally amend the ideas of formal concept analysis to accomodate signed/directed relations.

(Edit: reviewing my notes, the actual problem is somewhat worse than what I just described.

A typical signed-relation is something like "Markov taught Kolmogorov". But it's not enough to say that point-Markov is incident to line "teacher" with sign -1 (from or source) while point-Kolmogorov is incident to the same line with sign 1 (to or target). That merely establishes that Kolmogorov had teachers and Markov had students, but doesn't link both. So a signed relation is more like

$$G\times G \times \sigma, \quad M, \quad I\subset (G\times G\times M)$$

i.e. points are signed in a given signed-relation, not the incidence relation that binds them. But maybe this departs enough from incidence geometry that it's worth studying the $(G, M, I\times \sigma)$ "signed incidence structure" if it does come up in the literature.)

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