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A Comprehensive Formalization of Propositional Logic in Coq: Deduction Systems, Meta-Theorems, and Automation Tactics

https://doi.org/10.3390/math11112504
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-45949-9openalex-snapshot
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
inferredcites →https://doi.org/10.1007/978-3-030-32079-9_18openalex-snapshot
A Formally Verified Monitor for Metric First-Order Temporal Logic
inferredcites →https://doi.org/10.1007/978-3-030-79876-5_37openalex-snapshot
The Lean 4 Theorem Prover and Programming Language
inferredcites →https://doi.org/10.1007/978-3-030-89391-0_25openalex-snapshot
A Henkin-Style Completeness Proof for the Modal Logic S5
inferredcites →https://doi.org/10.1007/978-3-319-71237-6_10openalex-snapshot
Bringing Order to the Separation Logic Jungle
inferredcites →https://doi.org/10.1007/978-3-642-35308-6_22openalex-snapshot
Improving Real Analysis in Coq: A User-Friendly Approach to Integrals and Derivatives
inferredcites →https://doi.org/10.1007/978-3-642-39634-2_14openalex-snapshot
A Machine-Checked Proof of the Odd Order Theorem
inferredcites →https://doi.org/10.1007/978-3-662-05642-4_5openalex-snapshot
The Mechanization of Mathematics
inferredcites →https://doi.org/10.1007/s10817-009-9117-xopenalex-snapshot
An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps
inferredcites →https://doi.org/10.1007/s10817-009-9145-6openalex-snapshot
Formalizing an Analytic Proof of the Prime Number Theorem
inferredcites →https://doi.org/10.1007/s10817-017-9404-xopenalex-snapshot
A Formally Verified Proof of the Central Limit Theorem
inferredcites →https://doi.org/10.1017/fmp.2017.1openalex-snapshot
A FORMAL PROOF OF THE KEPLER CONJECTURE
inferredcites →https://doi.org/10.1038/d41586-021-01627-2openalex-snapshot
Mathematicians welcome computer-assisted proof in ‘grand unification’ theory
inferredcites →https://doi.org/10.1093/jigpal/jzaa007openalex-snapshot
Natural deduction and semantic models of justification logic in the proof assistant Coq
inferredcites →https://doi.org/10.1093/logcom/exaa073openalex-snapshot
Completeness theorems for first-order logic analysed in constructive type theory
inferredcites →https://doi.org/10.1109/cac48633.2019.8996365openalex-snapshot
A Formal Proof in Coq of Cantor-Bernstein-Schroeder’s Theorem without axiom of choice
inferredcites →https://doi.org/10.1145/2591012openalex-snapshot
Formally verified mathematics
inferredcites →https://doi.org/10.1145/2993600.2993611openalex-snapshot
Formal Verification of Smart Contracts
inferredcites →https://doi.org/10.1145/3167088openalex-snapshot
Completeness and decidability of converse PDL in the constructive type theory of Coq
inferredcites →https://doi.org/10.1145/3497775.3503684openalex-snapshot
Undecidability, incompleteness, and completeness of second-order logic in Coq
inferredcites →https://doi.org/10.1147/rd.41.0002openalex-snapshot
Toward Mechanical Mathematics
inferredcites →https://doi.org/10.1155/2021/5525539openalex-snapshot
CoCEC: An Automatic Combinational Circuit Equivalence Checker Based on the Interactive Theorem Prover
inferredcites →https://doi.org/10.1515/9780691197944-012openalex-snapshot
The Mechanization of Mathematics
inferredcites →https://doi.org/10.4204/eptcs.313.5openalex-snapshot
Teaching a Formalized Logical Calculus
inferredcites →https://doi.org/10.4204/eptcs.337.5openalex-snapshot
Countability of Inductive Types Formalized in the Object-Logic Level
inferredcites →https://doi.org/10.4204/eptcs.369.2openalex-snapshot
Mechanizing Matching Logic In Coq
inferredcites →https://doi.org/10.4230/lipics.itp.2022.19openalex-snapshot
Undecidability of Dyadic First-Order Logic in Coq
inferredcites →https://doi.org/10.48550/arxiv.0905.3713openalex-snapshot
A formal proof of the four color theorem
inferredcites →https://doi.org/10.48550/arxiv.cs/0505034openalex-snapshot
Essential Incompleteness of Arithmetic Verified by Coq

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/978-981-95-1106-8_13openalex-snapshot
Formalization of Gödel’s Completeness Theorem in Coq
inferred← citeshttps://doi.org/10.1007/978-981-95-1106-8_8openalex-snapshot
Formalization of Propositional Calculus Formal Systems in Coq
inferred← citeshttps://doi.org/10.1007/978-981-97-3951-6_11openalex-snapshot
Lagrange’s Theorem in Group Theory: Formalization and Proof with Coq
inferred← citeshttps://doi.org/10.1007/978-981-97-3951-6_5openalex-snapshot
Formal Proof of Meta-Theorem in First-Order Logic in Coq
inferred← citeshttps://doi.org/10.1007/978-981-97-3951-6_7openalex-snapshot
Formalizing the Independence of Propositional Logic Axiom System in Coq
inferred← citeshttps://doi.org/10.1007/978-981-97-3951-6_9openalex-snapshot
Formalizing the Equivalence of Formal Systems in Propositional Logic in Coq
inferred← citeshttps://doi.org/10.1007/s11424-026-5318-1openalex-snapshot
A Comparative Review of ZFC, NBG, and MK Axiom Systems: Theoretical Foundations and Formalization in Coq
inferred← citeshttps://doi.org/10.1061/jladah.ladr-1549openalex-snapshot
Mathematical Formalization of FIDIC Contract Provisions: A Propositional Logic Analysis of Risk Allocation Mechanisms in International Construction Contracting
inferred← citeshttps://doi.org/10.1109/access.2024.3501587openalex-snapshot
Toward Secure and Reliable IoT Systems: A Comprehensive Review of Formal Methods Applications
inferred← citeshttps://doi.org/10.1109/access.2025.3552634openalex-snapshot
A Review on Mechanical Proving and Formalization of Mathematical Theorems
inferred← citeshttps://doi.org/10.1109/cac59555.2023.10450918openalex-snapshot
Formalizing the Term Substitution Theorem in First-Order Logic within the Coq Proof Assistant
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