Semantical Analysis of Higher-Order Abstract Syntax
LICS '99 Proceedings of the 14th 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
A proof theory for generic judgments
ACM Transactions on Computational Logic (TOCL)
Consistency of the theory of contexts
Journal of Functional Programming
About permutation algebras, (pre)sheaves and named sets
Higher-Order and Symbolic Computation
On a monadic semantics for freshness
Theoretical Computer Science - Applied semantics: Selected topics
Cyclic proofs for first-order logic with inductive definitions
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
A unifying model of variables and names
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
A simpler proof theory for nominal logic
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
ACM Transactions on Programming Languages and Systems (TOPLAS)
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We propose a semantics for the @?-quantifier of Miller and Tiu. First we consider the case for classical first-order logic. In this case, the interpretation is close to standard Tarski-semantics and completeness can be shown using a standard argument. Then we put our semantics into a broader context by giving a general interpretation of @? in categories with binding structure. Since categories with binding structure also encompass nominal logic, we thus show that both @?-logic and nominal logic can be modelled using the same definition of binding. As a special case of the general semantics in categories with binding structure, we recover Gabbay & Cheney's translation of FO@l^@? into nominal logic.