From modal logic to terminal coalgebras
Theoretical Computer Science
Final coalgebras for functors on measurable spaces
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Final coalgebras for functors on measurable spaces
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Connections of coalgebra and semantic modeling
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Presenting functors by operations and equations
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Final sequences and final coalgebras for measurable spaces
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Taking it to the limit: approximate reasoning for markov processes
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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This paper connects coalgebra with a long discussion in the foundations of game theory on the modeling of type spaces. We argue that type spaces are coalgebras, that universal type spaces are final coalgebras, and that the modal logics already proposed in the economic theory literature are closely related to those in recent work in coalgebraic modal logic. In the other direction, the categories of interest in this work are usually measurable spaces or compact (Hausdorff) topological spaces. A coalgebraic version of the construction of the universal type space due to Heifetz and Samet [Journal of Economic Theory 82 (2) (1998) 324-341] is generalized for some functors in those categories. Since the concrete categories of interest have not been explored so deeply in the coalgebra literature, we have some new results. We show that every functor on the category of measurable spaces built from constant functors, products, coproducts, and the probability measure space functor has a final coalgebra. Moreover, we construct this final coalgebra from the relevant version of coalgebraic modal logic. Specifically, we consider the set of theories of points in all coalgebras and endow this set with a measurable and coalgebra structure.