Unified correspondence, proof-theoretically
This dissertation explores the connections between labelled sequent calculi and display calculi, two foundational proof-theoretic frameworks that, despite differences in syntax, structural constraints, and historical motivations, are shown to be deeply intertwined through the duality of their semantic underpinnings. Furthermore, it applies the two frameworks to investigate the properties of (D)LE logics. Central to this exploration is the transfer of ideas and techniques between these calculi via their semantic common ground, specifically relational and algebraic semantics.
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