Elf: a language for logic definition and verified metaprogramming
Proceedings of the Fourth Annual Symposium on Logic in computer science
A framework for defining logics
Journal of the ACM (JACM)
Logic programming in a fragment of intuitionistic linear logic
Papers presented at the IEEE symposium on Logic in computer science
Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Information and Computation
Free Deduction: An Analysis of "Computations" in Classical Logic
Proceedings of the First Russian Conference on Logic Programming
Using Linear Logic to Reason about Sequent Systems
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Specifying Theorem Provers in a Higher-Order Logic Programming Language
Proceedings of the 9th International Conference on Automated Deduction
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
On the specification of sequent systems
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Focusing and polarization in intuitionistic logic
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Incorporating tables into proofs
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Journal of Automated Reasoning
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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 focusingannotations 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.