30 citations · 72 across the 17 of their papers we have counts for
19 papers
Metric Equational Theories
Radu Mardare, Neil Ghani, Eigil Rischel
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET)…
Polynomial Lawvere Logic
Giorgio Bacci, Radu Mardare, Prakash Panangaden +1
We study Polynomial Lawvere logic PL, a logic defined over the Lawvere quantale of extended positive reals with sum as tensor, to which we add multiplication, thereby obtaining a s…
Propositional Logics for the Lawvere Quantale
Giorgio Bacci, Radu Mardare, Prakash Panangaden +1
Lawvere showed that generalised metric spaces are categories enriched over , the quantale of the positive extended reals. The statement of enrichment is a quantitative…
Sum and Tensor of Quantitative Effects
Giorgio Bacci, Radu Mardare, Prakash Panangaden +1
Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combinat…
Interpreting Lambda Calculus in Domain-Valued Random Variables
Robert Furber, Radu Mardare, Prakash Panangaden +1
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction r…
Fixed-Points for Quantitative Equational Logics
Radu Mardare, Prakash Panangaden, Gordon Plotkin
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-point…
Universal Semantics for the Stochastic Lambda-Calculus
Pedro Amorim, Dexter Kozen, Radu Mardare +2
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techn…
Computing Probabilistic Bisimilarity Distances for Probabilistic Automata
Giorgio Bacci, Giovanni Bacci, Kim G. Larsen +3
The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic…
Probabilistic logics based on Riesz spaces
Robert Furber, Radu Mardare, Matteo Mio
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of…
On the Metric-based Approximate Minimization of Markov Chains
Giovanni Bacci, Giorgio Bacci, Kim G. Larsen +1
In this paper, we address the approximate minimization problem of Markov Chains (MCs) from a behavioral metric-based perspective. Specifically, given a finite MC and a positive int…
On the Axiomatizability of Quantitative Algebras
Radu Mardare, Prakash Panangaden, Gordon Plotkin
Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016.…
Free complete Wasserstein algebras
Radu Mardare, Prakash Panangaden, Gordon D. Plotkin
We present an algebraic account of the Wasserstein distances on complete metric spaces, for . This is part of a program of a quantitative algebraic theory of effect…
Timed Comparisons of Semi-Markov Processes
Mathias Ruggaard Pedersen, Nathanaël Fijalkow, Giorgio Bacci +2
Semi-Markov processes are Markovian processes in which the firing time of the transitions is modelled by probabilistic distributions over positive reals interpreted as the probabil…
Reasoning About Bounds in Weighted Transition Systems
Mikkel Hansen, Kim Guldstrand Larsen, Radu Mardare +1
We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulatio…
On-the-Fly Computation of Bisimilarity Distances
Giorgio Bacci, Giovanni Bacci, Kim G. Larsen +1
We propose a distance between continuous-time Markov chains (CTMCs) and study the problem of computing it by comparing three different algorithmic methodologies: iterative, linear…
A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains
Giorgio Bacci, Giovanni Bacci, Kim G. Larsen +1
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in…
Topologies of Stochastic Markov Models: Computational Aspects
Giorgio Bacci, Giovanni Bacci, Kim G. Larsen +1
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems wher…
Parameterized Metatheory for Continuous Markovian Logic
Kim G. Larsen, Radu Mardare, Claus Thrane
This paper shows that a classic metalogical framework, including all Boolean operators, can be used to support the development of a metric behavioural theory for Markov processes.…
Continuous Markovian Logics - Axiomatization and Quantified Metatheory
Radu Mardare, Luca Cardelli, Kim G. Larsen
Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic)…