Abstract
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.
Original language | English |
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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 |
Pages | 189-200 |
ISBN (Print) | 1-59593-388-3 |
DOIs | |
Publication status | Published - 2006 |