The foundation of a generic theorem prover
Journal of Automated Reasoning
Binding Logic: Proofs and Models
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Proof Theory for Generic Judgments: An extended abstract
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
A Sequent Calculus for Nominal Logic
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Theoretical Computer Science
PPDP '05 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming
Information and Computation
A general mathematics of names
Information and Computation
A Logic for Reasoning about Generic Judgments
Electronic Notes in Theoretical Computer Science (ENTCS)
Combining Generic Judgments with Recursive Definitions
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Capture-avoiding substitution as a nominal algebra
Formal Aspects of Computing
Journal of Logic and Computation
A polynomial nominal unification algorithm
Theoretical Computer Science
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
The lambda-context calculus (extended version)
Information and Computation
Journal of Logic and Computation
A simpler proof theory for nominal logic
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Stone duality for nominal Boolean algebras with И
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Permissive-nominal logic: First-order logic over nominal terms and sets
ACM Transactions on Computational Logic (TOCL)
PNL to HOL: From the logic of nominal sets to the logic of higher-order functions
Theoretical Computer Science
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Permissive-Nominal Logic (PNL) is an extension of first-order logic where term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as the ∀l-quantifier of first-order logic itself and the λ-binder of the lambda-calculus. This also allows us to finitely axiomatise arithmetic. Like first- and higher-order logic and unlike other nominal logics, equality reasoning is not necessary to alpha-rename. All this gives PNL much of the expressive power of higher-order logic, but terms, derivations and models of PNL are first-order in character, and the logic seems to strike a good balance between expressivity and simplicity.