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International Conference on Numerical Computations: Theory and Algorithms

NUMTA 2019: Numerical Computations: Theory and Algorithms pp 43–58Cite as

A New Syntax for Diagrammatic Logic: A Generic Figures Approach

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

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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Notes

  1. 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. 2.

    Contravariant functors also reverse the direction of composition.

  3. 3.

    Restriction: for some n, \(F(A_n)=\emptyset \).

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Author information

Authors and Affiliations

  1. Endicott College, Beverly, MA, 01915, USA

    Gianluca Caterina & Rocco Gangle

Authors
  1. Gianluca Caterina
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  2. Rocco Gangle
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Corresponding author

Correspondence to Gianluca Caterina .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Caterina, G., Gangle, R. (2020). A New Syntax for Diagrammatic Logic: A Generic Figures Approach. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_4

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

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40615-8

  • Online ISBN: 978-3-030-40616-5

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