2 Search Results for "Docherty, Simon"

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DOI: 10.4230/LIPIcs.FSCD.2024.17

A Categorical Approach to DIBI Models

Authors: Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

The logic of Dependence and Independence Bunched Implications (DIBI) is a logic to reason about conditional independence (CI); for instance, DIBI formulas can characterise CI in discrete probability distributions and in relational databases, using a probabilistic DIBI model and a similarly-constructed relational model. Despite the similarity of the two models, there lacks a uniform account. As a result, the laborious case-by-case verification of the frame conditions required for constructing new models hinders them from generalising the results to CI in other useful models such that continuous distribution. In this paper, we develop an abstract framework for systematically constructing DIBI models, using category theory as the unifying mathematical language. We show that DIBI models arise from arbitrary symmetric monoidal categories with copy-discard structure. In particular, we use string diagrams - a graphical presentation of monoidal categories - to give a uniform definition of the parallel composition and subkernel relation in DIBI models. Our approach not only generalises known models, but also yields new models of interest and reduces properties of DIBI models to structures in the underlying categories. Furthermore, our categorical framework enables a comparison between string diagrammatic approaches to CI in the literature and a logical notion of CI, defined in terms of the satisfaction of specific DIBI formulas. We show that the logical notion is an extension of string diagrammatic CI under reasonable conditions.

Cite as

Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi. A Categorical Approach to DIBI Models. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gu_et_al:LIPIcs.FSCD.2024.17,
  author =	{Gu, Tao and Bao, Jialu and Hsu, Justin and Silva, Alexandra and Zanasi, Fabio},
  title =	{{A Categorical Approach to DIBI Models}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.17},
  URN =		{urn:nbn:de:0030-drops-203469},
  doi =		{10.4230/LIPIcs.FSCD.2024.17},
  annote =	{Keywords: Conditional Independence, Dependence Independence Bunched Implications, String Diagrams, Markov Categories}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2020.20

Partially Observable Concurrent Kleene Algebra

Authors: Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, and Alexandra Silva

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract

We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with variables as well as control structures, such as conditionals and loops, that depend on those variables. We illustrate the use of POCKA through concrete examples. We prove that POCKA is a sound and complete axiomatisation of a model of partial observations, and show the semantics passes an important check for sequential consistency.

Cite as

Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, and Alexandra Silva. Partially Observable Concurrent Kleene Algebra. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wagemaker_et_al:LIPIcs.CONCUR.2020.20,
  author =	{Wagemaker, Jana and Brunet, Paul and Docherty, Simon and Kapp\'{e}, Tobias and Rot, Jurriaan and Silva, Alexandra},
  title =	{{Partially Observable Concurrent Kleene Algebra}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.20},
  URN =		{urn:nbn:de:0030-drops-128324},
  doi =		{10.4230/LIPIcs.CONCUR.2020.20},
  annote =	{Keywords: Concurrent Kleene algebra, Kleene algebra with tests, observations, axiomatisation, completeness, sequential consistency}
}

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2 Silva, Alexandra
1 Bao, Jialu
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1 Gu, Tao
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2 Theory of computation → Semantics and reasoning
1 Theory of computation → Concurrency
1 Theory of computation → Formal languages and automata theory
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1 Theory of computation → Models of computation

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1 Concurrent Kleene algebra
1 Conditional Independence
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