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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) state-spaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates of the&nbsp;[&hellip;]

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On-the-Fly Computation of Bisimilarity Distances

Giorgio Bacci ; Giovanni Bacci ; Kim G. Larsen ; Radu Mardare.

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 program, and on-the-fly. In a work presented at FoSSaCS'12, Chen et al. characterized the bisimilarity distance of&nbsp;[&hellip;]

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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 this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of&nbsp;[&hellip;]

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Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

Giorgio Bacci ; Giovanni Bacci ; Kim G. Larsen ; Radu Mardare ; Qiyi Tang ; Franck van Breugel.

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 automata. In this paper, we present a characterization of the bisimilarity distance as the solution of a simple&nbsp;[&hellip;]

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Free complete Wasserstein algebras

Radu Mardare ; Prakash Panangaden ; Gordon D. Plotkin.

We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces, for $p \geq 1$. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in $p$, for algebras over metric spaces equipped&nbsp;[&hellip;]

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A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains

Giorgio Bacci ; Giovanni Bacci ; Kim G. Larsen ; Radu Mardare.

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 the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS&nbsp;[&hellip;]

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Reasoning About Bounds in Weighted Transition Systems

Mikkel Hansen ; Kim Guldstrand Larsen ; Radu Mardare ; Mathias Ruggaard Pedersen.

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 bisimulation that is coarser than the classic bisimulation: it relates states that exhibit transitions to bisimulation classes with&nbsp;[&hellip;]

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Sum and Tensor of Quantitative Effects

Giorgio Bacci ; Radu Mardare ; Prakash Panangaden ; Gordon Plotkin.

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 combination of quantitative algebraic effects. Quantitative algebraic effects are monadic computational effects on categories of&nbsp;[&hellip;]

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