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Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms Read chapter Read first chapter

2020 | OriginalPaper | Chapter

A New Syntax for Diagrammatic Logic: A Generic Figures Approach

Authors : Gianluca Caterina, Rocco Gangle

Published in: Numerical Computations: Theory and Algorithms

Publisher: Springer International Publishing

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Abstract

In this paper we propose a new syntactical representation of C.S. Peirce’s diagrammatic systems for propositional and predicate logic. In particular, we use the categorical notion of generic figures to represent the syntax of the diagrammatic language as a category of functors from a suitable, simple category into the category of sets, highlighting the relational nature of Peirce’s diagrammatic logic.

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Footnotes
1
This formulation only causes difficulties in the (not infrequent) cases when the objects and/or arrows of either \(\mathcal {C}\) or \(\mathcal {D}\) cannot be gathered into a set, for instance when one of these is the category Set of sets and functions. The ensuing problems and the various strategies for resolving them are readily located in the standard literature on categories.
 
2
Contravariant functors also reverse the direction of composition.
 
3
Restriction: for some n, \(F(A_n)=\emptyset \).
 
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Metadata
Title
A New Syntax for Diagrammatic Logic: A Generic Figures Approach
Authors
Gianluca Caterina
Rocco Gangle
Copyright Year
2020
Book
Numerical Computations: Theory and Algorithms

Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-40616-5_4

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