Conjecture on the superiority of minimal shallow embeddings for reasoning tasks

Determine whether minimal shallow embeddings of propositional modal logic in classical higher-order logic (HOL) are better suited than maximal shallow embeddings and deep embeddings for key reasoning tasks, specifically interactive and automated theorem proving and counterexample finding at both meta and object levels within Isabelle/HOL (including tools such as Sledgehammer and Nitpick).

Background

The paper introduces and links deep and shallow embeddings of propositional modal logic (PML) in classical higher-order logic (HOL), and shows automated faithfulness proofs between these embeddings in Isabelle/HOL. It contrasts maximal (heavyweight) and minimal (lightweight) shallow embeddings, highlighting differing degrees of explicitly maintained semantic dependencies.

Experiments reported later in the paper indicate that the minimal shallow embedding yielded better performance for automated proof search via Sledgehammer and counterexample generation via Nitpick across a variety of test statements, motivating a conjecture about its general suitability for certain reasoning tasks compared to maximal shallow and deep embeddings.