Abstract
Following the guiding thread of Peirce’s use of diagrammatic syntax in his system of existential graphs (EG), which depends crucially on the role of the Sheet of Assertion, we introduce the notion of Sheet of Indication (SI) as the basis for a general diagrammatic semantics applicable to a wide range of diagrams. We then show how Peirce’s EG-alpha graphs may be understood as instances of SIs and how logically coherent models of the graphs are represented in the SI semantics.
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Notes
Presheaves are fundamental constructions in category theory. In category-theoretical language, a presheaf is a contravariant functor from any category \(\mathcal {C}\) into \(\mathbf{Set}\), the category of sets and functions. The easiest example is given by considering the map \(\mathcal {F}(U)\) that takes any open set \(U\) of a topological space into the set of real-valued continuous functions over \(U\): given two open sets \(U\) and \(V\) (ordered by inclusion), with \(U\subseteq V\), there is a natural map between \(\mathcal {F(V)}\) onto \(\mathcal {F}(U)\) which takes an element \(f\in \mathcal {F}(V)\) (which is a map \(f:V\longrightarrow \mathbb {R}\)) onto the map \(f_{|U}\in \mathcal {F}(U)\), where \(f_{|U}\) is simply the restriction of \(f\) to \(U\).
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Gangle, R., Caterina, G. The sheet of indication: a diagrammatic semantics for Peirce’s EG-alpha. Synthese 192, 923–940 (2015). https://doi.org/10.1007/s11229-014-0495-1
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DOI: https://doi.org/10.1007/s11229-014-0495-1