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Aggregate Programming through a Soft Modal Logic Alberto Lluch Lafuente Based on joint work with Ugo Montanari (University of Pisa) Michele Loreti (University of Florence) Martin Rasmussen (DTU) LMU, May 24, 2016

Aggregate Programming through a Soft Modal Logic

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Page 1: Aggregate Programming through a Soft Modal Logic

Aggregate�Programming�through�a�Soft�Modal�Logic��

Alberto�Lluch�Lafuente��

Based�on�joint�work�with�Ugo�Montanari�(University�of�Pisa)�

Michele�Loreti�(University�of�Florence)�Martin�Rasmussen�(DTU)��

�

LMU,May24,2016

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LMU,May24,2016

Whatis“aggregateprogramming”?

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foldr f z [] = z foldr f z (x:xs) = f x (foldr f z xs)

MPI_Reduce(&sum,...);

SELECT COUNT(*) FROM ...

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LMU,May24,2016

Asoftmodallogicforaggregateprogramming

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⟦ ⟧ ∃ ⟦ ⟧

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⟦ ⟧ ∃ ⟦ ⟧

⟦ ⟧ ⋁ ⟦ ⟧

⟦ ⟧ 𝔹

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⟦ ⟧ ∃ ⟦ ⟧

⟦ ⟧ ⋁ ⟦ ⟧

∃

⟦ ⟧ 𝔹

⟦∃ ⟧ ⋁ ⟦ ⟧

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⟦ ⟧ ∃ ⟦ ⟧

⟦ ⟧ ⋁ ⟦ ⟧

∃

⟦ ⟧ 𝔹

⟦∃ ⟧ ⋁ ⟦ ⟧

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⟦ ⟧ ∃ ⟦ ⟧

⟦ ⟧ ⋁ ⟦ ⟧

∃

⟦ ⟧ 𝔹

⟦∃ ⟧ ⋁ ⟦ ⟧

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LMU,May24,2016

Addingrecursion

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⨆ ⨆

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⨆ ⨆

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⨆ ⨆

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LMU,May24,2016

Combiningqueries

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ϵ

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ϵ

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LMU,May24,2016

CoordinationOfAgents

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LMU,May24,2016

GraphDataAnalytics

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LMU,May24,2016

Distributedcomputations

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⨆ ⨆

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LMU,May24,2016

Wrappingup

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QUESTIONS?��

[email protected]��

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LMU,May24,2016

Page 63: Aggregate Programming through a Soft Modal Logic

Semantical Considerations on Modal Logic

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