WADT'22 - 26th International Workshop on Algebraic Development Techniques 2022

Aveiro, 28 - 30 June 2022

Plenary Talk: On Phenomenology of Computation

This talk is an overall presentation of Quantitative Algebras (QA), which I have introduced with Panangaden and Plotkin in 2016. QAs generalize universal algebras by developing an equational theory where the congruences on terms are approximated. In effect, one gets algebraic structures over metric spaces, axiomatic representations of metrics, monads on the category of metric spaces (generalizing the classic monads on SET that one obtains from the classic universal algebras) and more. The classic variety and quasi-variety results are extended, and we present stronger versions of Birkhoff's theorems. Finally, we developed a metric-based version of Conway and iteration theories, extending Plotkin-Power's axiomatic presentation of fixed-point theories. QAs provide a novel foundation for computational paradigms and a quantitative algebraic theory of effects. Applied to the field of cyber-physical systems, QAs bring the possibility of speaking of approximated models, which allows one to measure and control the errors induced by the imperfect information (e.g., from measuring real-valued data) and how these imperfections can alter the predicted behaviour of a system. The topology induced by the metric structure allows one to speak of "better-and-better" models of a cyber-physical system and to measure the behavioural differences between a real system and its imperfect model.

Radu Mardare (Department of Computer & Information Sciences, University of Strathclyde, Glasgow)

Radu Mardare is a professor at the Department of Computer & Information Sciences, University of Strathclyde, Glasgow. His research interest covers fields from logics and model theory to algebras, coalgebras, topology and measure theory; as well as foundations of mathematics from classic and non-standard set theory to category theory, with a focus on models of computation. He has worked extensively on modelling and analysing probabilistic and stochastic systems. He promotes the idea of a semantics for computational systems based on continuous mathematics, as an alternative to the classic Boolean and discrete semantics. The goal is to integrate concepts like approximations, convergence, behavioural similarities, integration into the core of computational paradigms. Webpage

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The conference is supported by CIDMA through the Portuguese Foundation for Science and Technology, reference UIDB/04106/2020