Theoretical Computer Science
Basic proof theory
Labelled proof systems for intuitionistic provability
Labelled deduction
A Local System for Classical Logic
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
A Schütte-Tait Style Cut-Elimination Proof for First-Order Gödel Logic
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Maude as a Platform for Designing and Implementing Deep Inference Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
On the proof complexity of deep inference
ACM Transactions on Computational Logic (TOCL)
An Algorithmic Interpretation of a Deep Inference System
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Deep Inference in Bi-intuitionistic Logic
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Nested proof search as reduction in the Lambda-calculus
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
A hypersequent system for gödel-dummett logic with non-constant domains
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Reducing nondeterminism in the calculus of structures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Atomic Lambda Calculus: A Typed Lambda-Calculus with Explicit Sharing
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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This paper presents systems for first-order intuitionistic logic and several of its extensions in which all the propositional rules are local, in the sense that, in applying the rules of the system, one needs only a fixed amount of information about the logical expressions involved. The main source of non-locality is the contraction rules. We show that the contraction rules can be restricted to the atomic ones, provided we employ deep-inference, i.e., to allow rules to apply anywhere inside logical expressions. We further show that the use of deep inference allows for modular extensions of intuitionistic logic to Dummett's intermediate logic LC, Gödel logic and classical logic. We present the systems in the calculus of structures, a proof theoretic formalism which supports deep-inference. Cut elimination for these systems are proved indirectly by simulating the cut-free sequent systems, or the hypersequent systems in the cases of Dummett's LC and Gödel logic, in the cut free systems in the calculus of structures.