Gentzen-type systems and resolution rules. Part I. Propositional logic
COLOG-88 Proceedings of the international conference on Computer logic
Specifying coalgebras with modal logic
Theoretical Computer Science
Modal logic
A New Method for Bounding the Complexity of Modal Logics
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
Labelled Tableaux for Non-normal Modal Logics
AI*IA '99 Proceedings of the 6th Congress of the Italian Association for Artificial Intelligence on Advances in Artificial Intelligence
Canonical Propositional Gentzen-Type Systems
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
PSPACE Bounds for Rank-1 Modal Logics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A sequent calculus and a theorem prover for standard conditional logics
ACM Transactions on Computational Logic (TOCL)
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
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
A Coalgebraic Perspective on Monotone Modal Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Rank-1 modal logics are coalgebraic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A finite model construction for coalgebraic modal logic
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Optimal Tableaux for Conditional Logics with Cautious Monotonicity
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Flat coalgebraic fixed point logics
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Global caching for coalgebraic description logics
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Coalgebraic predicate logic: equipollence results and proof theory
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
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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We give two generic proofs for cut elimination in propositional modal logics, interpreted over coalgebras. We first investigate semantic coherence conditions between the axiomatisation of a particular logic and its coalgebraic semantics that guarantee that the cut-rule is admissible in the ensuing sequent calculus. We then independently isolate a purely syntactic property of the set of modal rules that guarantees cut elimination. Apart from the fact that cut elimination holds, our main result is that the syntactic and semantic assumptions are equivalent in case the logic is amenable to coalgebraic semantics. As applications we present a new proof of the (already known) interpolation property for coalition logic and newly establish the interpolation property for the conditional logics LCK and LCKID.