Convex Power Constructions for Continuous D-Cones

Tix, Regina

doi:10.1016/s1571-0661(05)01217-x

Cited by 6 publications

(9 citation statements)

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“…In particular, the convex powerdomains of spaces of measures on X was studied by Mislove [31], by Tix et al [39,40], and by Morgan and McIver [30].…”

Section: Related Workmentioning

confidence: 99%

Static Analysis of Programs with Imprecise Probabilistic Inputs

Adjé

Bouissou

Goubault-Larrecq

et al. 2014

Verified Software: Theories, Tools, Experiments

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Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about programs with inputs given as imprecise probabilities: we define a collecting semantics based on the notion of previsions and an abstract semantics based on an extension of Dempster-Shafer structures. We prove the correctness of our approach and show on some realistic examples the kind of invariants we are able to infer.

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“…In particular, the convex powerdomains of spaces of measures on X was studied by Mislove [31], by Tix et al [39,40], and by Morgan and McIver [30].…”

Section: Related Workmentioning

confidence: 99%

Static Analysis of Programs with Imprecise Probabilistic Inputs

Adjé

Bouissou

Goubault-Larrecq

et al. 2014

Verified Software: Theories, Tools, Experiments

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“…What the right way is to combine non-determinism with probabilistic choice has been a long-standing question in programming language semantics, cf. [13,23,27,28]. Notably, for example, there is no distributive law in Set of the non-determinism monad over the probabilistic choice monad and none in the opposite direction either 1 .…”

Section: Applicationsmentioning

confidence: 99%

Coproducts of Ideal Monads

Ghani

Uustalu

2004

RAIRO-Theor. Inf. Appl.

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“…In previous work, [Jon90,Hec96,Tix99], the probabilistic powerdomain has been characterised as a free cone over the space . It is would be interesting to see if this characterization can be used to prove completeness of our axiomatization without referring to the spatial side at all.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

A Logic for Probabilities in Semantics

Moshier

Jung

2002

Computer Science Logic

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Probabilistic computation has proven to be a challenging and interesting area of research, both from the theoretical perspective of denotational semantics and the practical perspective of reasoning about probabilistic algorithms. On the theoretical side, the probabilistic powerdomain of Jones and Plotkin represents a significant advance. Further work, especially by Alvarez-Manilla, has greatly improved our understanding of the probabilistic powerdomain, and has helped clarify its relation to classical measure and integration theory. On the practical side, many researchers such as Kozen, Segala, Desharnais, and Kwiatkowska, among others, study problems of verification for probabilistic computation by defining various suitable logics for the classes of processes under study. The work reported here begins to bridge the gap between the domain theoretic and verification (model checking) perspectives on probabilistic computation by exhibiting sound and complete logics for probabilistic powerdomains that arise directly from given logics for the underlying domains.The category in which the construction is carried out generalizes Scott's Information Systems by taking account of full classical sequents. Via Stone duality, following Abramsky's Domain Theory in Logical Form, all known interesting categories of domains are embedded as subcategories. So the results reported here properly generalize similar constructions on specific categories of domains. The category offers a promising universe of semantic domains characterized by a very rich structure and good preservation properties of standard constructions. Furthermore, because the logical constructions make use of full classical sequents, the morphisms have a natural non-deterministic interpretation. Thus the category is a natural one in which to investigate the relationship between probabilistic and non-deterministic computation. We discuss the problem of integrating probabilistic and non-deterministic computation after presenting the construction of logics for probabilistic powerdomains.

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Convex Power Constructions for Continuous D-Cones

Cited by 6 publications

References 0 publications

Static Analysis of Programs with Imprecise Probabilistic Inputs

Static Analysis of Programs with Imprecise Probabilistic Inputs

Coproducts of Ideal Monads

A Logic for Probabilities in Semantics

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