On the complexity of epistemic reasoning
Proceedings of the Fourth Annual Symposium on Logic in computer science
Abstract and concrete categories
Abstract and concrete categories
Bisimulation through probabilistic testing
Information and Computation
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Bisimulation for probabilistic transition systems: a coalgebraic approach
Theoretical Computer Science
Journal of the ACM (JACM)
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Modal logic
Time and Probability in Formal Design of Distributed Systems
Time and Probability in Formal Design of Distributed Systems
Alternating-time temporal logic
Journal of the ACM (JACM)
Inductive Datatypes in HOL - Lessons Learned in Formal-Logic Engineering
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Reasoning about Uncertainty
ε-connections of abstract description systems
Artificial Intelligence
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
A sequent calculus and a theorem prover for standard conditional logics
ACM Transactions on Computational Logic (TOCL)
Modular construction of complete coalgebraic logics
Theoretical Computer Science
Expressivity of coalgebraic modal logic: The limits and beyond
Theoretical Computer Science
Shallow Models for Non-iterative Modal Logics
KI '08 Proceedings of the 31st annual German conference on Advances in Artificial Intelligence
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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
Rank-1 Modal Logics are Coalgebraic
Journal of Logic and Computation
Probability and nondeterminism in operational models of concurrency
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Optimal tableau algorithms for coalgebraic logics
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Global caching for coalgebraic description logics
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Modular algorithms for heterogeneous modal logics
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
On the fusion of coalgebraic logics
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Coalgebraic announcement logics
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. In this paper, we show that the combination of features can be reflected algorithmically, and we develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying state-based systems as multi-sorted coalgebras and associating both a logical and algorithmic description with a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided this is also the case for the components. By instantiating the general framework to concrete cases, we obtain PSpace decision procedures for a wide variety of structurally different logics, describing, for example, Segala systems and games with uncertain information.