Researchers have developed three distinct embeddings for monadic second-order logic (MSO) within the Isabelle/HOL theorem prover. These embeddings include a deep embedding, a maximal-shallow embedding, and a minimal-shallow embedding, each with specific translation methodologies. A key innovation is a two-sorted substitution apparatus that facilitates capture-avoiding substitution and renaming, with a substitution lemma for each namespace. The faithfulness of these embeddings has been mechanized and automated, leading to a fully mechanized two-sorted downward Loewenheim-Skolem theorem. AI
RANK_REASON The cluster contains a research paper detailing new methodologies and theorems within formal logic and theorem proving. [lever_c_demoted from research: ic=1 ai=0.4]
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