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.

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

3. LMU, May 24, 2016
What is
“aggregate
programming”?

6. foldr f z [] = z
foldr f z (x:xs) = f x (foldr f z xs)
MPI_Reduce(&sum,...);
SELECT COUNT(*) FROM ...

7. LMU, May 24, 2016
A soft modal
logic for
aggregate
programming

8. ⟦ ⟧ ∃ ⟦ ⟧

9. ⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
⟦ ⟧ 𝔹

10. ⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
∃
⟦ ⟧ 𝔹
⟦∃ ⟧ ⋁ ⟦ ⟧

11. ⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
∃
⟦ ⟧ 𝔹
⟦∃ ⟧ ⋁ ⟦ ⟧

12. ⟦ ⟧ ∃ ⟦ ⟧
⟦ ⟧ ⋁ ⟦ ⟧
∃
⟦ ⟧ 𝔹
⟦∃ ⟧ ⋁ ⟦ ⟧

21. LMU, May 24, 2016
Adding
recursion

22. ⨆ ⨆

23. ⨆ ⨆

24. ⨆ ⨆

25. ⨆ ⨆

26. ⨆ ⨆

31. LMU, May 24, 2016
Combining
queries

36. ϵ
⨆ ⨆

37. ϵ
⨆ ⨆

38. ⨆ ⨆

39. ⨆ ⨆

41. LMU, May 24, 2016
Coordination
Of Agents

44. LMU, May 24, 2016
Graph Data
Analytics

47. LMU, May 24, 2016
Distributed
computations

52. ⨆ ⨆

53. ⨆ ⨆

54. ⨆ ⨆

55. ⨆ ⨆

56. ⨆ ⨆

57. LMU, May 24, 2016
Wrapping up

62. QUESTIONS?
albl@dtu.dk
LMU, May 24, 2016