A Note on Proper Relational Structures

This paper was the first piece of work made public on my research into simplicial semantics for modal logic after the initial technical report. The reason this paper was pushed out first is that the main result was needed to be cited in the second technical report, currently forthcoming.

This paper is not obviously connected to simplicial semantics, however. What this paper provides is a general tool for closing certain gaps in more complicated completeness proofs in the simplicial literature. Generally, completeness in that setting is shown first by generating a canonical Kripke model which is translated into a simplicial model. However, the general techniques for creating canonical Kripke models do not always create a mdoel which can be so translated. Our main result in this paper provides a way of transforming canonical models in such a way that the output is bisimilar, but the output is guaranteed to be translateable into a simplicial model under most translation functions.

Recommended citation: Adam Bjorndahl and Philip Sink (2025). "A Note on Proper Relational Structures" arXiv
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