Fixed-Points for Quantitative Equational Logics

We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of approximate equality rather than exact equality. The result is a n...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Authors: Mardare, Radu, Panangaden, Prakash, Plotkin, Gordon
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Algebra
Computer science
Convergence
Extraterrestrial measurements
Markov processes
Semantics
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Summary:We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of approximate equality rather than exact equality. The result is a novel theory of fixed points which can not only provide solutions to the traditional fixed-point equations but we can also define the rate of convergence to the fixed point. We show that such a theory is the quantitative analogue of a Conway theory and also of an iteration theory; and it reflects the metric coinduction principle. We study the Bellman equation for a Markov decision process as an illustrative example.
DOI:10.1109/LICS52264.2021.9470662