Fixed-Points for Quantitative Equational Logics

Radu Mardare, Prakash Panangaden, Gordon D Plotkin

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.
Original languageEnglish
Title of host publicationProceedings of the 36th Annual Symposium on Logic in Computer Science
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages13
ISBN (Electronic)978-1-6654-4895-6
ISBN (Print)978-1-6654-4896-3
Publication statusPublished - 9 Jul 2021
Event36th Annual ACM/IEEE Symposium on Logic in Computer Science - Online
Duration: 29 Jun 20212 Jul 2021


Symposium36th Annual ACM/IEEE Symposium on Logic in Computer Science
Abbreviated titleLICS 2021
Internet address


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