5 Search Results for "Marsden, Dan"

Document
DOI: 10.4230/LIPIcs.MFCS.2022.7
Comonadic semantics for hybrid logic

Authors: Samson Abramsky and Dan Marsden

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Hybrid logic is a widely-studied extension of basic modal logic, which corresponds to the bounded fragment of first-order logic. We study it from two novel perspectives: (1) We apply the recently introduced paradigm of comonadic semantics, which provides a new set of tools drawing on ideas from categorical semantics which can be applied to finite model theory, descriptive complexity and combinatorics. (2) We give a novel semantic characterization of hybrid logic in terms of invariance under disjoint extensions, a minimal form of locality. A notable feature of this result is that we give a uniform proof, valid for both the finite and infinite cases.
Cite as

Samson Abramsky and Dan Marsden. Comonadic semantics for hybrid logic. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{abramsky_et_al:LIPIcs.MFCS.2022.7,
  author =	{Abramsky, Samson and Marsden, Dan},
  title =	{{Comonadic semantics for hybrid logic}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.7},
  URN =		{urn:nbn:de:0030-drops-168055},
  doi =		{10.4230/LIPIcs.MFCS.2022.7},
  annote =	{Keywords: comonads, model comparison games, semantic characterizations, hybrid logic, bounded fragment}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.115
Arboreal Categories and Resources

Authors: Samson Abramsky and Luca Reggio

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We introduce arboreal categories, which have an intrinsic process structure, allowing dynamic notions such as bisimulation and back-and-forth games, and resource notions such as number of rounds of a game, to be defined. These are related to extensional or "static" structures via arboreal covers, which are resource-indexed comonadic adjunctions. These ideas are developed in a very general, axiomatic setting, and applied to relational structures, where the comonadic constructions for pebbling, Ehrenfeucht-Fraïssé and modal bisimulation games recently introduced in [Abramsky et al., 2017; S. Abramsky and N. Shah, 2018; Abramsky and Shah, 2021] are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers.
Cite as

Samson Abramsky and Luca Reggio. Arboreal Categories and Resources. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abramsky_et_al:LIPIcs.ICALP.2021.115,
  author =	{Abramsky, Samson and Reggio, Luca},
  title =	{{Arboreal Categories and Resources}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{115:1--115:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.115},
  URN =		{urn:nbn:de:0030-drops-141845},
  doi =		{10.4230/LIPIcs.ICALP.2021.115},
  annote =	{Keywords: factorisation system, embedding, comonad, coalgebra, open maps, bisimulation, game, resources, relational structures, finite model theory}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.77
Preservation of Equations by Monoidal Monads

Authors: Louis Parlant, Jurriaan Rot, Alexandra Silva, and Bas Westerbaan

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
If a monad T is monoidal, then operations on a set X can be lifted canonically to operations on TX. In this paper we study structural properties under which T preserves equations between those operations. It has already been shown that any monoidal monad preserves linear equations; affine monads preserve drop equations (where some variable appears only on one side, such as x⋅ y = y) and relevant monads preserve dup equations (where some variable is duplicated, such as x ⋅ x = x). We start the paper by showing a converse: if the monad at hand preserves a drop equation, then it must be affine. From this, we show that the problem whether a given (drop) equation is preserved is undecidable. A converse for relevance turns out to be more subtle: preservation of certain dup equations implies a weaker notion which we call n-relevance. Finally, we identify a subclass of equations such that their preservation is equivalent to relevance.
Cite as

Louis Parlant, Jurriaan Rot, Alexandra Silva, and Bas Westerbaan. Preservation of Equations by Monoidal Monads. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{parlant_et_al:LIPIcs.MFCS.2020.77,
  author =	{Parlant, Louis and Rot, Jurriaan and Silva, Alexandra and Westerbaan, Bas},
  title =	{{Preservation of Equations by Monoidal Monads}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{77:1--77:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.77},
  URN =		{urn:nbn:de:0030-drops-127460},
  doi =		{10.4230/LIPIcs.MFCS.2020.77},
  annote =	{Keywords: monoidal monads, algebraic theories, preservation of equations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.32
Quantitative Foundations for Resource Theories

Authors: Dan Marsden and Maaike Zwart

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Considering resource usage is a powerful insight in the analysis of many phenomena in the sciences. Much of the current research on these resource theories focuses on the analysis of specific resources such quantum entanglement, purity, randomness or asymmetry. However, the mathematical foundations of resource theories are at a much earlier stage, and there has been no satisfactory account of quantitative aspects such as costs, rates or probabilities. We present a categorical foundation for quantitative resource theories, derived from enriched category theory. Our approach is compositional, with rich algebraic structure facilitating calculations. The resulting theory is parameterized, both in the quantities under consideration, for example costs or probabilities, and in the structural features of the resources such as whether they can be freely copied or deleted. We also achieve a clear separation of concerns between the resource conversions that are freely available, and the costly resources that are typically the object of study. By using an abstract categorical approach, our framework is naturally open to extension. We provide many examples throughout, emphasising the resource theoretic intuitions for each of the mathematical objects under consideration.
Cite as

Dan Marsden and Maaike Zwart. Quantitative Foundations for Resource Theories. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{marsden_et_al:LIPIcs.CSL.2018.32,
  author =	{Marsden, Dan and Zwart, Maaike},
  title =	{{Quantitative Foundations for Resource Theories}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.32},
  URN =		{urn:nbn:de:0030-drops-96996},
  doi =		{10.4230/LIPIcs.CSL.2018.32},
  annote =	{Keywords: Resource Theory, Enriched Category, Profunctor, Monad, Combinatorial Species, Multicategory, Operad, Bimodule}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2017.17
Custom Hypergraph Categories via Generalized Relations

Authors: Dan Marsden and Fabrizio Genovese

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

Abstract
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical systems and network theory. When investigating a new application, the question arises of how to identify a suitable process theoretic model. We present a conceptually motivated parameterized framework for the construction of models for process theories. Our framework generalizes the notion of binary relation along four axes of variation, the truth values, a choice of algebraic structure, the ambient mathematical universe and the choice of proof relevance or provability. The resulting categories are preorder-enriched and provide analogues of relational converse and taking graphs of maps. Our constructions are functorial in the parameter choices, establishing mathematical connections between different application domains. We illustrate our techniques by constructing many existing models from the literature, and new models that open up ground for further development.
Cite as

Dan Marsden and Fabrizio Genovese. Custom Hypergraph Categories via Generalized Relations. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{marsden_et_al:LIPIcs.CALCO.2017.17,
  author =	{Marsden, Dan and Genovese, Fabrizio},
  title =	{{Custom Hypergraph Categories via Generalized Relations}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.17},
  URN =		{urn:nbn:de:0030-drops-80494},
  doi =		{10.4230/LIPIcs.CALCO.2017.17},
  annote =	{Keywords: Process Theory, Categorical Compositional Semantics, Generalized Relations, Hypergraph Category, Compact Closed Category}
}
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