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Aggregate Programming through a Soft Modal Logic
Alberto Lluch Lafuente
Based on joint work with
Ugo Montanari (University...
LMU,	May	24,	2016	
What	is	
“aggregate		
		programming”?
foldr f z [] = z
foldr f z (x:xs) = f x (foldr f z xs)
MPI_Reduce(&sum,...);
SELECT COUNT(*) FROM ...
LMU,	May	24,	2016	
A	soft	modal	
logic	for	
aggregate	
programming
⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
⟦ ⟧ 𝔹
⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
∃
⟦ ⟧ 𝔹
⟦∃ ⟧ ⋁ ⟦ ⟧
⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
∃
⟦ ⟧ 𝔹
⟦∃ ⟧ ⋁ ⟦ ⟧
⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
∃
⟦ ⟧ 𝔹
⟦∃ ⟧ ⋁ ⟦ ⟧
LMU,	May	24,	2016	
Adding	
recursion
⨆ ⨆
⨆ ⨆
⨆ ⨆
⨆ ⨆
⨆ ⨆
LMU,	May	24,	2016	
Combining	
queries
ϵ
⨆ ⨆
ϵ
⨆ ⨆
⨆ ⨆
⨆ ⨆
LMU,	May	24,	2016	
Coordination	
Of	Agents
LMU,	May	24,	2016	
Graph	Data	
Analytics
LMU,	May	24,	2016	
Distributed	
computations
⨆ ⨆
⨆ ⨆
⨆ ⨆
⨆ ⨆
⨆ ⨆
LMU,	May	24,	2016	
Wrapping	up
QUESTIONS?
albl@dtu.dk
	
	
LMU,	May	24,	2016
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
Aggregate Programming through a Soft Modal Logic
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Aggregate Programming through a Soft Modal Logic

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Talk at the Informatics Colloquium at LMU München.

Abstract: Aggregation plays a central role in many computational paradigms and their applications. Classical examples are fold/reduce functions in functional programming, reduce/gather operations in parallel programming, and set functions in database programming. Aggregation is essential as well in many of today's IT trends, from Big (Graph) Data analytics to coordination of devices and services in complex distributed systems such as the Internet-of-Things. Aggregate programming models, languages and techniques are indeed a current topic of research in several communities. I will discuss how a soft variant of a modal logic can provide a convenient declarative approach to aggregate programming and I will mention applications to distributed coordination of agents and to distributed graph analytics.

Published in: Science
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Aggregate Programming through a Soft Modal Logic

  1. 1. 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
  2. 2. LMU, May 24, 2016 What is “aggregate programming”?
  3. 3. foldr f z [] = z foldr f z (x:xs) = f x (foldr f z xs) MPI_Reduce(&sum,...); SELECT COUNT(*) FROM ...
  4. 4. LMU, May 24, 2016 A soft modal logic for aggregate programming
  5. 5. ⟦ ⟧ ∃ ⟦ ⟧
  6. 6. ⟦ ⟧ ∃ ⟦ ⟧ ⟦ ⟧ ⋁ ⟦ ⟧ ⟦ ⟧ 𝔹
  7. 7. ⟦ ⟧ ∃ ⟦ ⟧ ⟦ ⟧ ⋁ ⟦ ⟧ ∃ ⟦ ⟧ 𝔹 ⟦∃ ⟧ ⋁ ⟦ ⟧
  8. 8. ⟦ ⟧ ∃ ⟦ ⟧ ⟦ ⟧ ⋁ ⟦ ⟧ ∃ ⟦ ⟧ 𝔹 ⟦∃ ⟧ ⋁ ⟦ ⟧
  9. 9. ⟦ ⟧ ∃ ⟦ ⟧ ⟦ ⟧ ⋁ ⟦ ⟧ ∃ ⟦ ⟧ 𝔹 ⟦∃ ⟧ ⋁ ⟦ ⟧
  10. 10. LMU, May 24, 2016 Adding recursion
  11. 11. ⨆ ⨆
  12. 12. ⨆ ⨆
  13. 13. ⨆ ⨆
  14. 14. ⨆ ⨆
  15. 15. ⨆ ⨆
  16. 16. LMU, May 24, 2016 Combining queries
  17. 17. ϵ ⨆ ⨆
  18. 18. ϵ ⨆ ⨆
  19. 19. ⨆ ⨆
  20. 20. ⨆ ⨆
  21. 21. LMU, May 24, 2016 Coordination Of Agents
  22. 22. LMU, May 24, 2016 Graph Data Analytics
  23. 23. LMU, May 24, 2016 Distributed computations
  24. 24. ⨆ ⨆
  25. 25. ⨆ ⨆
  26. 26. ⨆ ⨆
  27. 27. ⨆ ⨆
  28. 28. ⨆ ⨆
  29. 29. LMU, May 24, 2016 Wrapping up
  30. 30. QUESTIONS? albl@dtu.dk LMU, May 24, 2016

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