Abstract
In this paper we show how to represent any modal function (i.e. a function expressed by a formula of the propositional modal logic S5) as a tuple of truth-functions, and we provide a nice graphical representation of the modal functions in terms of colorations of edges of certain complete bipartite graphs.
I express my gratitude to Rodrigo Ramos for the fruitful discussions that we had on the topics presented here, and for the great help he provided while turning this material into the LaTeX format. I would also like to thank Roderick Batchelor, Melina Bertholdo, Luiza Ramos, Tomás Troster, and the reviewers for their comments on the preliminary versions of this paper, and Levi Magalhães for the enthusiasm we shared when considering the prototypes of these diagrams.
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References
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Falcão, P. (2021). New Representations of Modal Functions. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_28
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DOI: https://doi.org/10.1007/978-3-030-86062-2_28
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