Abstract
In this paper, we present and exemplify the Basic Graph Logic (BGL), this is an initial formalism which can be extended to provide a diagrammatic representation within which Set Theory and, hence, the whole of mathematics can be diagrammatic developed. We present the syntax, semantics, and inference engine of BGL. We introduce and exemplify the BGL-inference rules by showing, throughout diagrammatic proofs, that the BGL-operators satisfy the analogous of the relation algebra axioms, i.e., BGL is build as a distributive complemented lattice with operators satisfying the involutive monoid axioms and the De Morgan’s Theorem K.
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Cerioli, M.R., Suguitani, L., Viana, P. (2021). Presenting Basic Graph Logic. 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_12
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DOI: https://doi.org/10.1007/978-3-030-86062-2_12
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