Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Bisimulation through probabilistic testing
Information and Computation
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Modal logic
Automata and Algebras in Categories
Automata and Algebras in Categories
Alternating-time temporal logic
Journal of the ACM (JACM)
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
Expressivity of coalgebraic modal logic: The limits and beyond
Theoretical Computer Science
Automata and fixed point logic: A coalgebraic perspective
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
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
Cut elimination in coalgebraic logics
Information and Computation
A Note on Expressive Coalgebraic Logics for Finitary Set Functors
Journal of Logic and Computation
Rank-1 Modal Logics are Coalgebraic
Journal of Logic and Computation
Cut elimination for shallow modal logics
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
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We show that all (not necessarily normal or monotone) modal logics that can be axiomatised in rank-1 have the interpolation property, and that in fact interpolation is uniform if the logics just have finitely many modal operators. As immediate applications, we obtain previously unknown interpolation theorems for a range of modal logics, containing probabilistic and graded modal logic, alternating temporal logic and some variants of conditional logic. Technically, this is achieved by translating to and from a new (coalgebraic) logic introduced in this paper, the logic of exact covers. It is interpreted over coalgebras for an endofunctor on the category of sets that also directly determines the syntax. Apart from closure under bisimulation quantifiers (and hence interpolation), we also provide a complete tableaux calculus and establish both the Hennessy-Milner and the small model property for this logic.