Basic proof theory (2nd ed.)
A Calculus and Complexity Bound for Minimal Conditional Logic
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Efficient Loop-Check for Backward Proof Search in Some Non-classical Propositional Logics
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Canonical Propositional Gentzen-Type Systems
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A sequent calculus and a theorem prover for standard conditional logics
ACM Transactions on Computational Logic (TOCL)
Towards an algorithmic construction of cut-elimination procedures†
Mathematical Structures in Computer Science
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
Memory bounds for recognition of context-free and context-sensitive languages
FOCS '65 Proceedings of the 6th Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1965)
Generic Modal Cut Elimination Applied to Conditional Logics
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Beyond rank 1: algebraic semantics and finite models for coalgebraic logics
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Sequent systems for lewis' conditional logics
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
The Logic of Exact Covers: Completeness and Uniform Interpolation
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Motivated by the fact that nearly all conditional logics are axiomatised by so-called shallow axioms (axioms with modal nesting depth ≤ 1) we investigate sequent calculi and cut elimination for modal logics of this type. We first provide a generic translation of shallow axioms to (one-sided, unlabelled) sequent rules. The resulting system is complete if we admit pseudo-analytic cut, i.e. cuts on modalised propositional combinations of subformulas, leading to a generic (but sub-optimal) decision procedure. In a next step, we show that, for finite sets of axioms, only a small number of cuts is needed between any two applications of modal rules. More precisely, completeness still holds if we restrict to cuts that form a tree of logarithmic height between any two modal rules. In other words, we obtain a small (PSPACE-computable) representation of an extended rule set for which cut elimination holds. In particular, this entails PSPACE decidability of the underlying logic if contraction is also admissible. This leads to (tight) PSPACE bounds for various conditional logics.