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Faithful Logic Embeddings in HOL -- Deep and Shallow

2025/02/26 by Christoph Benzmüller, Benzmüller, Christoph
Computer Science · #03Axx #03B15 #03Bxx #68T15 #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #F.4 #FOS: Computer and information sciences #FOS: Mathematics #I.2.3 #I.2.4 #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.2502.19311

openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep and shallow embeddings of various degrees in classical higher-order logic. This enables flexible, interactive and automated theorem proving and counterexample finding at meta and object level, as well as automated faithfulness proofs between these logic embeddings. The method is beneficial for logic education, research and application and is illustrated here using a simple propositional modal logic. However, this approach is conceptual in nature and not limited to this simple logic context.

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