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)
ACM Transactions on Computational Logic (TOCL)
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
Nominal Algebra and the HSP Theorem
Journal of Logic and Computation
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
Journal of Logic and Computation
A formal calculus for informal equality with binding
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
A simpler proof theory for nominal logic
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
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Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatizations with binders, such as of the λ-binder of the lambda-calculus or the ∀-binder of first-order logic. It also allows us to finitely axiomatize arithmetic, and similarly to axiomatize “nominal” datatypes-with-binding. Just like first- and higher-order logic, equality reasoning is not necessary to α-rename. This gives PNL much of the expressive power of higher-order logic, but models and derivations of PNL are first-order in character, and the logic seems to strike a good balance between expressivity and simplicity.