Basic proof theory
The method of hypersequents in the proof theory of propositional non-classical logics
Logic: from foundations to applications
First-order modal logic
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Modular Sequent Systems for Modal Logic
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Taming Displayed Tense Logics Using Nested Sequents with Deep Inference
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
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
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This paper introduces a nested sequent system for predicate logic. The system features a structural universal quantifier and a universally closed existential rule. One nice consequence of this is that proofs of sentences cannot contain free variables. Another nice consequence is that the assumption of a non-empty domain is isolated in a single inference rule. This rule can be removed or added at will, leading to a system for free logic or classical predicate logic, respectively. The system for free logic is interesting because it has no need for an existence predicate. We see syntactic cut-elimination and completeness results for these two systems as well as two standard applications: Herbrand's Theorem and interpolation.