Diagrammatic Algebra of First Order Logic

Alessandro Di Giorgio; Filippo Bonchi; Nathan Haydon; Pawel Sobocinski

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

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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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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.

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