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Diagrammatic Algebra of First Order Logic

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arxiv 2401.07055 v1 pith:TBNQDN33 submitted 2024-01-13 cs.LO math.CT

Filippo Bonchi , Alessandro Di Giorgio , Nathan Haydon , Pawel Sobocinski This is my paper · ORCID
classification cs.LOmath.CT
keywords calculusdiagrammaticfirstlogicorderrelationsalgebraaxiomatisation
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We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained by combining two well known categorical structures: cartesian and linear bicategories.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Principled Solution to the Disjunction Problem of Diagrammatic Query Representations

    cs.DB 2024-12 conditional novelty 7.0 of 10

    RepresentationB is a query diagram system that achieves the first pattern-complete diagrammatic representation of well-formed Tuple Relational Calculus with arbitrary disjunctions.

  2. Foundations of Digital Circuits: Denotation, Operational, and Algebraic Semantics

    cs.LO 2025-02 conditional novelty 6.0 of 10

    A sound and complete denotational, operational, and algebraic semantics for synchronous sequential circuits with arbitrary feedback, plus a hypergraph rewriting framework for digital circuits.

  3. Logical Aspects of Virtual Double Categories

    math.CT 2025-01 conditional novelty 6.0 of 10

    Elementary existential fibrations correspond exactly to cartesian equipments obtained via the new /BU il construction, and regular fibrations correspond to those with Beck-Chevalley pullbacks.

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