The practice of first-order logic is replete with meta-level concepts. Most notably there are the meta-variables themselves (ranging over predicates, variables, and terms), assumptions about freshness of variables with respect to these meta-variables, alpha-equivalence and capture-avoiding substitution. We present one-and-a-halfth-order logic, in which these concepts are made explicit. We exhibit both algebraic and sequent specifications of one-and-a-halfth-order logic derivability, show them equivalent, show that the derivations satisfy cut-elimination, and prove correctness of an interpretation of first-order logic within itWe discuss the technicalities in a wider context as a case-study for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation for future implementation.
|Title of host publication||Proceedings 8th ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming (PPDP'06, Venice, Italy, July 10-12, 2006)|
|Place of Publication||New York|
|Publisher||Association for Computing Machinery, Inc|
|Publication status||Published - 2006|