The Power of Peircean Algebraic Logic (PAL)

  • Joachim Hereth Correia
  • Reinhard Pöschel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2961)

Abstract

The existential graphs devised by Charles S. Peirce can be understood as an approach to represent and to work with relational structures long before the manifestation of relational algebras as known today in modern mathematics. Robert Burch proposed in [Bur91] an algebraization of the existential graphs and called it the Peircean Algebraic Logic (PAL). In this paper, we show that the expressive power of PAL is equivalent to the expressive power of Krasner-algebras (which extend relational algebras). Therefore, from the mathematical point of view these graphs can be considered as a two-dimensional representation language for first-order formulas. Furthermore, we investigate the special properties of the teridentity in this framework and Peirce’s thesis, that to build all relations out of smaller ones we need at least a relation of arity three (for instance, the teridentity itself).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Joachim Hereth Correia
    • 1
  • Reinhard Pöschel
    • 2
  1. 1.Department of MathematicsDarmstadt University of TechnologyDarmstadtGermany
  2. 2.Department of Mathematics, Institute for AlgebraDresden University of TechnologyDresdenGermany

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