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Towards Ideal Semantics for Analyzing Stream Reasoning Harald Beck - - PowerPoint PPT Presentation

Oct 19, 2023 142 likes •1.76k views

Towards Ideal Semantics for Analyzing Stream Reasoning Harald Beck Minh Dao-Tran Thomas Eiter Michael Fink International Workshop on Reactive Concepts in Knowledge Representation 2014 August 19, 2014 Scope & Motivation Windows &

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SLIDE 1

Towards Ideal Semantics for Analyzing Stream Reasoning

Harald Beck Minh Dao-Tran Thomas Eiter Michael Fink International Workshop on Reactive Concepts in Knowledge Representation 2014 August 19, 2014

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SLIDE 2

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 3

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 4

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 5

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

◮ Semantics

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 6

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

◮ Semantics: Lack of theory

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 7

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

◮ Semantics: Lack of theory ◮ Analysis

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

slide-8
SLIDE 8

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

◮ Semantics: Lack of theory ◮ Analysis: Hard to predict, hard to compare

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 9

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

◮ Semantics: Lack of theory ◮ Analysis: Hard to predict, hard to compare ◮ Ideal

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 10

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

What & Why

“Towards Ideal Semantics for Analyzing Stream Reasoning”

◮ Stream Reasoning: Logical reasoning on streaming data

◮ Streams = tuples (atoms) with timestamps ◮ Essential aspect: window functions

◮ Semantics: Lack of theory ◮ Analysis: Hard to predict, hard to compare ◮ Ideal

◮ Idealization: Abstract from practical (operational) issues ◮ Generalization: Uniform representation

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 1 / 15

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SLIDE 11

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 12

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 13

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) 2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 14

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) 2 8

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 15

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) 2 8

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 16

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) 2 8 11

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 17

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 18

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 19

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 20

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

Answer: i1, i2, p1

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 21

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

Answer: i1, i2, p1 and i3, i4, p2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 22

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

Answer: i1, i2, p1 and i3, i4, p2

◮ SQL

SELECT * FROM tram, bus WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 23

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

Answer: i1, i2, p1 and i3, i4, p2

◮ SQL

SELECT * FROM tram, bus WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 24

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

Answer: i1, i2, p1 and i3, i4, p2

◮ SQL

SELECT * FROM tram, bus WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 25

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2)

◮ Normal DB: Query for trams and buses arriving at same station P

Answer: i1, i2, p1 and i3, i4, p2

◮ SQL

SELECT * FROM tram, bus WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 26

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream setting, at time 13: Query for

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 27

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream setting, at time 13: Query for ◮ Trams and buses arriving at same station P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 28

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream setting, at time 13: Query for ◮ Trams and buses arriving at same station P within the last 5 min

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 29

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream setting, at time 13: Query for ◮ Trams and buses arriving at same station P within the last 5 min

Answer: i3, i4, p2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 30

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream setting, at time 13: Query for ◮ Trams and buses arriving at same station P within the last 5 min

Answer: i3, i4, p2

◮ CQL

SELECT * FROM tram [RANGE 5], bus [RANGE 5] WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 31

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Trams and buses arriving at same station P within the last 5 min

at the same time

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 32

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Trams and buses arriving at same station P within the last 5 min

at the same time Answer: –

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

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SLIDE 33

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13 3 4 5 6 7

◮ Trams and buses arriving at same station P within the last 5 min

at the same time Answer: i1, i2, p1 for query times 2, . . . , 7

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

slide-34
SLIDE 34

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Trams and buses arriving at same station P within the last 5 min

at the same time Answer: i1, i2, p1 for query times 2, . . . , 7

◮ CQL: Not expressible in single query (Snapshot semantics)

SELECT * AS tram bus FROM tram [NOW], bus [NOW] WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

slide-35
SLIDE 35

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) 2 8 11 13

◮ Trams and buses arriving at same station P within the last 5 min

at the same time Answer: i1, i2, p1 for query times 2, . . . , 7

◮ CQL: Not expressible in single query (Snapshot semantics)

SELECT * AS tram bus FROM tram [NOW], bus [NOW] WHERE tram.P = bus.P

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

slide-36
SLIDE 36

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) 2 8 11 13

◮ Trams and buses arriving at same station P within the last 5 min

at the same time Answer: i1, i2, p1 for query times 2, . . . , 7

◮ CQL: Not expressible in single query (Snapshot semantics)

SELECT * AS tram bus FROM tram [NOW], bus [NOW] WHERE tram.P = bus.P SELECT * FROM tram bus [RANGE 5]

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

slide-37
SLIDE 37

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Trams and buses

Arrival times at different stations pi

tram(i1, p1) bus(i2, p1) 2 8 11 13

◮ Trams and buses arriving at same station P within the last 5 min

at the same time Answer: i1, i2, p1 for query times 2, . . . , 7

◮ CQL: Not expressible in single query (Snapshot semantics)

SELECT * AS tram bus FROM tram [NOW], bus [NOW] WHERE tram.P = bus.P SELECT * FROM tram bus [RANGE 5]

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 2 / 15

slide-38
SLIDE 38

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Window Types

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Time-based

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 3 / 15

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SLIDE 39

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Window Types

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Time-based ◮ Tuple-based

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 3 / 15

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SLIDE 40

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Window Types

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Time-based ◮ Tuple-based

◮ Not necessarily unique. E.g.: Last 3 tuples

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 3 / 15

slide-41
SLIDE 41

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Window Types

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Time-based ◮ Tuple-based

◮ Not necessarily unique. E.g.: Last 3 tuples

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 3 / 15

slide-42
SLIDE 42

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Window Types

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Time-based ◮ Tuple-based

◮ Not necessarily unique. E.g.: Last 3 tuples

◮ Partition-based

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 3 / 15

slide-43
SLIDE 43

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Window Types

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Time-based ◮ Tuple-based

◮ Not necessarily unique. E.g.: Last 3 tuples

◮ Partition-based

◮ Apply tuple-based window on substreams

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 3 / 15

slide-44
SLIDE 44

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?”

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-45
SLIDE 45

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?”

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-46
SLIDE 46

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?” ◮ Allow for nesting: windows within windows

◮ As formal counterpart to repeated runs of continuous queries

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-47
SLIDE 47

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?” ◮ Allow for nesting: windows within windows

◮ As formal counterpart to repeated runs of continuous queries

◮ Allow for looking into the future

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-48
SLIDE 48

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?” ◮ Allow for nesting: windows within windows

◮ As formal counterpart to repeated runs of continuous queries

◮ Allow for looking into the future ◮ View window operators as first class citizens

◮ Do not separate window application (first) from logic (then)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-49
SLIDE 49

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?” ◮ Allow for nesting: windows within windows

◮ As formal counterpart to repeated runs of continuous queries

◮ Allow for looking into the future ◮ View window operators as first class citizens

◮ Do not separate window application (first) from logic (then)

◮ Leave open specific underlying window functions

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-50
SLIDE 50

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Windows

◮ Example: “In the last hour, did a bus always arrive within 5 min?” ◮ Allow for nesting: windows within windows

◮ As formal counterpart to repeated runs of continuous queries

◮ Allow for looking into the future ◮ View window operators as first class citizens

◮ Do not separate window application (first) from logic (then)

◮ Leave open specific underlying window functions

◮ w(S, t) → S′ ◮ Stream S, time point t ∈ N, new stream S′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 4 / 15

slide-51
SLIDE 51

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 1 2 3 4 5 6

a a a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-52
SLIDE 52

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. 1 2 3 4 5 6

a a a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-53
SLIDE 53

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-54
SLIDE 54

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .
  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-55
SLIDE 55

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-56
SLIDE 56

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-57
SLIDE 57

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-58
SLIDE 58

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-59
SLIDE 59

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-60
SLIDE 60

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-61
SLIDE 61

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-62
SLIDE 62

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′? ♦ a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-63
SLIDE 63

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′? ♦ a yes

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-64
SLIDE 64

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′? ♦ a yes . . . at all time points t′?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-65
SLIDE 65

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′? ♦ a yes . . . at all time points t′? a

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-66
SLIDE 66

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′? ♦ a yes . . . at all time points t′? a no

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-67
SLIDE 67

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Ideas for Time Reference

◮ Atoms a appearing in the stream at time points 1, 2, 5 ◮ Query time t = 4. Window on interval [1, 4] 1 2 3 4 5 6

a a a

  • ◮ Example queries: In this window, does a hold. . .

. . . now, i.e., exactly at t? a no . . . at time point 2? @2 a yes . . . at some time point t′? ♦ a yes . . . at all time points t′? a no

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 5 / 15

slide-68
SLIDE 68

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream S = (T, υ), where

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-69
SLIDE 69

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream S = (T, υ), where

◮ T: interval in N

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-70
SLIDE 70

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-71
SLIDE 71

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

◮ Example

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-72
SLIDE 72

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

◮ Example

◮ T = [0, 13]

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-73
SLIDE 73

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 8 11 13 2

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

◮ Example

◮ T = [0, 13] ◮ υ =

2 → {tram(i1, p1), bus(i2, p1)}

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-74
SLIDE 74

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 11 13 8

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

◮ Example

◮ T = [0, 13] ◮ υ =

2 → {tram(i1, p1), bus(i2, p1)}, 8 → {tram(i3, p2)}

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-75
SLIDE 75

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 13 11

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

◮ Example

◮ T = [0, 13] ◮ υ =

2 → {tram(i1, p1), bus(i2, p1)}, 8 → {tram(i3, p2)}, 11 → {bus(i4, p2)}

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-76
SLIDE 76

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Streams

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

◮ Stream S = (T, υ), where

◮ T: interval in N ◮ υ : T → 2G (interpretation of ground atoms G)

◮ Example

◮ T = [0, 13] ◮ υ =

2 → {tram(i1, p1), bus(i2, p1)}, 8 → {tram(i3, p2)}, 11 → {bus(i4, p2)}, i → ∅ else

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 6 / 15

slide-77
SLIDE 77

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::=

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-78
SLIDE 78

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-79
SLIDE 79

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α | ♦α | α | @tα

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-80
SLIDE 80

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α | ♦α | α | @tα | ⊞iα

◮ ⊞i window operator: change view on stream

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-81
SLIDE 81

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α | ♦α | α | @tα | ⊞iα

◮ ⊞i window operator: change view on stream

◮ Utilizing window function with identifier i

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-82
SLIDE 82

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α | ♦α | α | @tα | ⊞iα

◮ ⊞i window operator: change view on stream

◮ Utilizing window function with identifier i ◮ Change considered substream based on current time point, and ◮ current window, or ◮ original stream

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-83
SLIDE 83

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α | ♦α | α | @tα | ⊞iα

◮ ⊞i window operator: change view on stream

◮ Utilizing window function with identifier i ◮ Change considered substream based on current time point, and ◮ current window, or ◮ original stream ◮ Window operator = window function + stream choice function

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-84
SLIDE 84

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Formulas

◮ Formulas defined by the grammar (atom a, t ∈ N timepoint)

α ::= a | ¬α | α ∧ α | α ∨ α | α → α | ♦α | α | @tα | ⊞iα

◮ ⊞i window operator: change view on stream

◮ Utilizing window function with identifier i ◮ Change considered substream based on current time point, and ◮ current window, or ◮ original stream ◮ Window operator = window function + stream choice function ◮ Why keep the original stream?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 7 / 15

slide-85
SLIDE 85

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram bus tram bus 2 8 11 13

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-86
SLIDE 86

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram bus tram bus 2 8 11 13

◮ Partition-based window

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-87
SLIDE 87

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram bus tram bus 2 8 11 13

◮ Partition-based window

◮ Partition stream into substreams: trams vs. buses

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-88
SLIDE 88

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram tram 2 8 13

◮ Partition-based window

◮ Partition stream into substreams: trams vs. buses ◮ Apply tuple-based windows on substreams: 2 trams, 0 buses

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-89
SLIDE 89

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram tram 2 8 13

◮ Partition-based window

◮ Partition stream into substreams: trams vs. buses ◮ Apply tuple-based windows on substreams: 2 trams, 0 buses

◮ In the new view, buses are invisible

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-90
SLIDE 90

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram tram 2 8 7 13

◮ Partition-based window

◮ Partition stream into substreams: trams vs. buses ◮ Apply tuple-based windows on substreams: 2 trams, 0 buses

◮ In the new view, buses are invisible ◮ ⇒ For “within 5 min” window: use data of original stream again

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-91
SLIDE 91

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Nested Windows and Stream Choice

◮ “For the last two trams, did a bus always appear within 5 min?”

tram bus tram bus 2 8 7 13 11

◮ Partition-based window

◮ Partition stream into substreams: trams vs. buses ◮ Apply tuple-based windows on substreams: 2 trams, 0 buses

◮ In the new view, buses are invisible ◮ ⇒ For “within 5 min” window: use data of original stream again

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 8 / 15

slide-92
SLIDE 92

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-93
SLIDE 93

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-94
SLIDE 94

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream ◮ ˆ

W mapping from idenfiers (in N) to extended window functions

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-95
SLIDE 95

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream ◮ ˆ

W mapping from idenfiers (in N) to extended window functions

◮ choice function ch(S1, S2) → S′

ˆ w(S1, S2, t) = w(ch(S1, S2), t)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-96
SLIDE 96

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream ◮ ˆ

W mapping from idenfiers (in N) to extended window functions

◮ choice function ch(S1, S2) → S′

ˆ w(S1, S2, t) = w(ch(S1, S2), t)

◮ Example

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-97
SLIDE 97

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream ◮ ˆ

W mapping from idenfiers (in N) to extended window functions

◮ choice function ch(S1, S2) → S′

ˆ w(S1, S2, t) = w(ch(S1, S2), t)

◮ Example

◮ w5 time-based window for last 5 minutes

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-98
SLIDE 98

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream ◮ ˆ

W mapping from idenfiers (in N) to extended window functions

◮ choice function ch(S1, S2) → S′

ˆ w(S1, S2, t) = w(ch(S1, S2), t)

◮ Example

◮ w5 time-based window for last 5 minutes ◮ ch2 choice that selects the second stream (ch2(S1, S2) = S2)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-99
SLIDE 99

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Structure

◮ Structure M = T, υ, ˆ

W, where

◮ (T, υ) original stream ◮ ˆ

W mapping from idenfiers (in N) to extended window functions

◮ choice function ch(S1, S2) → S′

ˆ w(S1, S2, t) = w(ch(S1, S2), t)

◮ Example

◮ w5 time-based window for last 5 minutes ◮ ch2 choice that selects the second stream (ch2(S1, S2) = S2) ◮ ˆ

W(1) = ˆ w5, where ˆ w5(S1, S2, t) = w5(S2, t)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 9 / 15

slide-100
SLIDE 100

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-101
SLIDE 101

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-102
SLIDE 102

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-103
SLIDE 103

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-104
SLIDE 104

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

M, S, t a iff a ∈ υS(t) ,

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-105
SLIDE 105

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

M, S, t a iff a ∈ υS(t) , M, S, t ¬α iff M, S, t α, M, S, t α ∧ β iff M, S, t α and M, S, t β, M, S, t α ∨ β iff M, S, t α or M, S, t β, M, S, t α → β iff M, S, t α or M, S, t β,

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-106
SLIDE 106

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

M, S, t a iff a ∈ υS(t) , M, S, t ¬α iff M, S, t α, M, S, t α ∧ β iff M, S, t α and M, S, t β, M, S, t α ∨ β iff M, S, t α or M, S, t β, M, S, t α → β iff M, S, t α or M, S, t β, M, S, t ♦α iff M, S, t′ α for some t′ ∈ TS,

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-107
SLIDE 107

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

M, S, t a iff a ∈ υS(t) , M, S, t ¬α iff M, S, t α, M, S, t α ∧ β iff M, S, t α and M, S, t β, M, S, t α ∨ β iff M, S, t α or M, S, t β, M, S, t α → β iff M, S, t α or M, S, t β, M, S, t ♦α iff M, S, t′ α for some t′ ∈ TS, M, S, t α iff M, S, t′ α for all t′ ∈ TS ,

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-108
SLIDE 108

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

M, S, t a iff a ∈ υS(t) , M, S, t ¬α iff M, S, t α, M, S, t α ∧ β iff M, S, t α and M, S, t β, M, S, t α ∨ β iff M, S, t α or M, S, t β, M, S, t α → β iff M, S, t α or M, S, t β, M, S, t ♦α iff M, S, t′ α for some t′ ∈ TS, M, S, t α iff M, S, t′ α for all t′ ∈ TS , M, S, t @t′α iff M, S, t′ α and t′ ∈ TS ,

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-109
SLIDE 109

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Semantics: Entailment

◮ Structure M = T, υ, ˆ

W with original stream SM = (T, υ)

◮ Substream S = (TS, υS) of SM: currently considered window ◮ Time point t ∈ TS (query time) ◮ Entailment between M, S, t and formulas α, β

M, S, t a iff a ∈ υS(t) , M, S, t ¬α iff M, S, t α, M, S, t α ∧ β iff M, S, t α and M, S, t β, M, S, t α ∨ β iff M, S, t α or M, S, t β, M, S, t α → β iff M, S, t α or M, S, t β, M, S, t ♦α iff M, S, t′ α for some t′ ∈ TS, M, S, t α iff M, S, t′ α for all t′ ∈ TS , M, S, t @t′α iff M, S, t′ α and t′ ∈ TS , M, S, t ⊞iα iff M, S′, t α where S′ = ˆ wi(SM, S, t).

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 10 / 15

slide-110
SLIDE 110

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-111
SLIDE 111

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-112
SLIDE 112

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 bus(i2, p1)?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-113
SLIDE 113

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

tram(i1, p1) tram(i3, p2) bus(i4, p2) bus(i2, p1) 2 8 11 13

M, SM, 13 bus(i2, p1), since bus(i2, p1) ∈ υ(13)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-114
SLIDE 114

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 ♦bus(i2, p1)?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-115
SLIDE 115

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

tram(i1, p1) tram(i3, p2) bus(i4, p2) bus(i2, p1) 8 11 13 2

M, SM, 13 ♦bus(i2, p1), since ∃ t′ ∈ TSM s.t. bus(i2, p1) ∈ υ(t′)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

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SLIDE 116

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

⊞1: last 5 min

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 ⊞1♦ bus(i2, p1)?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-117
SLIDE 117

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

⊞1: last 5 min

tram(i1, p1) tram(i3, p2) bus(i4, p2) bus(i2, p1) 13 2 8 9 10 11 12 13

M, SM, 13 ⊞1♦ bus(i2, p1)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

slide-118
SLIDE 118

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Queries

◮ Query α[t]: “M, SM, t α”?

⊞1: last 5 min

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13 9 10 12

M, SM, 13 ⊞1♦ bus(i4, p2)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 11 / 15

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SLIDE 119

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

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SLIDE 120

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-121
SLIDE 121

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 ⊞1♦bus(X, P)?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

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SLIDE 122

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 ⊞1♦bus(X, P)? X → i4, P → p2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-123
SLIDE 123

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, S, U ⊞1♦bus(i2, p1)?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-124
SLIDE 124

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) tram(i3, p2) bus(i4, p2) bus(i2, p1) 8 11 13 2 3 4 5 6 7

M, S, U ⊞1♦bus(i2, p1)? U → 2, . . . , 7

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-125
SLIDE 125

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 9 10 11 12 13

M, SM, 13 ⊞1(♦tram(X, P) ∧ ♦bus(Y, P))?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-126
SLIDE 126

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 ⊞1(♦tram(X, P) ∧ ♦bus(Y, P))? X → i3, P → p2, Y → i4

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-127
SLIDE 127

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, U ⊞1♦(tram(X, P) ∧ bus(Y, P))?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-128
SLIDE 128

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i3, p2) bus(i4, p2) tram(i1, p1) bus(i2, p1) 8 11 13 2 3 4 5 6 7

M, SM, U ⊞1♦(tram(X, P) ∧ bus(Y, P))? U → 2, . . . , 7 × X → i1, P → p1, Y → i2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-129
SLIDE 129

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i1, p1) bus(i2, p1) tram(i3, p2) bus(i4, p2) 2 8 11 13

M, SM, 13 @U(tram(X, P)) ∧ bus(Y, P))?

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-130
SLIDE 130

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Non-ground Queries

◮ Non-ground query: Assignments s.t. substitution hold

tram(i3, p2) bus(i4, p2) tram(i1, p1) bus(i2, p1) 8 11 13 2

M, SM, 13 @U(tram(X, P)) ∧ bus(Y, P))? U → 2, X → i1, P → p1, Y → i2

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 12 / 15

slide-131
SLIDE 131

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-132
SLIDE 132

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

◮ ⊞i: time-based window for last i minutes

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-133
SLIDE 133

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-134
SLIDE 134

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-135
SLIDE 135

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60 ⊞5

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-136
SLIDE 136

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60 ⊞5 ♦

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-137
SLIDE 137

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus bus bus 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60 ⊞5 ♦ bus

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-138
SLIDE 138

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus(i, p) bus(j, q) bus(k, r) 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60 ⊞5 ♦ bus ◮ Limitation: ⊞60 ⊞5 ♦ bus(X, P)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

slide-139
SLIDE 139

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Example: Nested Window

◮ “In the last hour, did a bus always appear in the last 5 minutes?”

bus(i, p) bus(j, q) bus(k, r) 206 213 217 t

◮ ⊞i: time-based window for last i minutes ◮ Query: ⊞60 ⊞5 ♦ bus ◮ Limitation: ⊞60 ⊞5 ♦ bus(X, P)

◮ Result: List of fixed combinations X, P ◮ Need a rule: some bus ← bus(X, P) ◮ Then: ⊞60 ⊞5 ♦some bus

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 13 / 15

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SLIDE 140

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

t − k

◮ Past

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

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SLIDE 141

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? t − k

◮ Past: Lack of theoretical underpinning for stream reasoning

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-142
SLIDE 142

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? t − k t (now)

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

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SLIDE 143

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) t − k t (now)

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-144
SLIDE 144

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) t − k t (now) t + ε

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-145
SLIDE 145

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) b ← a t − k t (now) t + ε

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon: Rule-based extension (OrdRing @ ISWC, Oct.’14)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-146
SLIDE 146

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) b ← a t − k t (now) t + ε t + n

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon: Rule-based extension (OrdRing @ ISWC, Oct.’14) ◮ Later

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-147
SLIDE 147

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) b ← a CQL, ETALIS properties t − k t (now) t + ε t + n

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon: Rule-based extension (OrdRing @ ISWC, Oct.’14) ◮ Later: Language properties, capture CQL and ETALIS

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-148
SLIDE 148

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) b ← a CQL, ETALIS properties t − k t (now) t + ε t + n t + n + m

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon: Rule-based extension (OrdRing @ ISWC, Oct.’14) ◮ Later: Language properties, capture CQL and ETALIS ◮ Eventually

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-149
SLIDE 149

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) b ← a CQL, ETALIS properties distributed t − k t (now) t + ε t + n t + n + m

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon: Rule-based extension (OrdRing @ ISWC, Oct.’14) ◮ Later: Language properties, capture CQL and ETALIS ◮ Eventually: Distributed setting, heterogeneous nodes

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-150
SLIDE 150

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

Conclusion Stream

? | = ? ⊞(a ∧ ♦b) b ← a CQL, ETALIS properties distributed t − k t (now) t + ε t + n t + n + m

◮ Past: Lack of theoretical underpinning for stream reasoning ◮ Now: First language for modelling semantics precisely

◮ flexible window operator (first class citizen) ◮ time reference / time abstraction

◮ Soon: Rule-based extension (OrdRing @ ISWC, Oct.’14) ◮ Later: Language properties, capture CQL and ETALIS ◮ Eventually: Distributed setting, heterogeneous nodes

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 14 / 15

slide-151
SLIDE 151

Scope & Motivation Windows & Time Framework Examples Conclusion & Outlook

To je ono.

(That’s it.)

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 15 / 15

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SLIDE 152

Appendix

Time-based window

◮ Example

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-153
SLIDE 153

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-154
SLIDE 154

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • d
  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-155
SLIDE 155

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • ×
  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-156
SLIDE 156

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • ×
  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-157
SLIDE 157

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • ×

ℓ

  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-158
SLIDE 158

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • ×
  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-159
SLIDE 159

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • × u
  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-160
SLIDE 160

Appendix

Time-based window

◮ Example: Query time t = 4

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • ×
  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15

slide-161
SLIDE 161

Appendix

Time-based window

◮ Example

ℓ 2 time points into the past u 1 time points into the future d 3 step size (slide parameter)

1 2 3 4 5 6 7 8 9

  • ×

× × ×

  • ×

× ×

  • ×

× ×

  • : query times t

×: pivot points t′

  • H. Beck (TU Vienna)

Towards Ideal Semantics for Analyzing Stream Reasoning ReactKnow’14 16 / 15