This book constitutes the refereed proceedings of the 19th International Conference on Unity of Logic and Computation, CiE 2023, held in Batumi, Georgia, during July 24–28, 2023. The 23 full papers and 13 invited papers included in this book were carefully reviewed and selected from 51 submissions. Proof Theory;

​Degree theory.- Cupping computably enumerable degrees simultaneously.- The relationship between local and global structure in the enumeration degrees.- A directed system of Scott ideals.- Proof Theory.- The non-normal abyss in Kleene's computability theory.- A Constructive Picture of Noetherianity and Well Quasi-Orders.- Computability.- Symmetry for transfinite computability.- All Melodies are Lost -- Recognizability for weak and strong α-ITRMs.- The de Groot dual of represented spaces.- Algorithmic Randomness.- Some Games on Turing Machines and Power from Random Strings.- Inequalities for entropies and dimensions.- Computational Complexity.- Elementarily traceable irrational numbers.- Logic vs topology on regular ω-languages.- Subrecursive Graphs of Representations of Irrational Numbers.- On the complexity of learning programs.- The Weihrauchcomplexity of the supergraph problem.- Extending Wagner's hierarchy to Deterministic Visibly Pushdown Automata.- On guarded extensions of MMSNP.- Turning block-sequential automata networks into smaller parallel networks with isomorphic limit dynamics.- Interactive proofs.- Structural Complexity of Rational Interactive Proofs.- Physical Zero-Knowledge Proof for Ball Sort Puzzle.- Combinatorial approaches.- Graph subshifts.- Improved Complexity Analysis of Quasi-Polynomial Algorithms Solving Parity Games.- An O(√k)-approximation algorithm for minimum power k edge disjoint st-paths.

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