It is well known how to use an intuitionistic meta-logic to specify natural deduction systems. It is also possible to use linear logic as a meta-logic for the specification of a variety of sequent calculus proof systems. Here, we show that if we adopt different focusing annotations for such linear logic specifications, a range of other proof systems can also be specified. In particular, we show that natural deduction (normal and non-normal), sequent proofs (with and without cut), tableaux, and proof systems using general elimination and general introduction rules can all be derived from essentially the same linear logic specification by altering focusing annotations. By using elementary linear logic equivalences and the completeness of focused proofs, we are able to derive new and modular proofs of the soundness and completeness of these various proofs systems for intuitionistic and classical logics. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Nigam, V., & Miller, D. (2008). Focusing in linear meta-logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5195 LNAI, pp. 507–522). https://doi.org/10.1007/978-3-540-71070-7_42
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