Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences...

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Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge Processing Research Group Concept Analysis at Darmstadt University of Technology

Transcript of Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences...

Page 1: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Temporal Concept Logic Objects, States, and Systems

Karl Erich Wolff

University of Applied Sciences Darmstadt

Ernst Schröder Center

for Conceptual Knowledge Processing

Research Group Concept Analysis at

Darmstadt University of Technology

Page 2: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Old Unsolved Problems in Temporal Logic

Aristotle asked (Vol. 6, book III – VI):

What is the meaning of ...

• movement, change

• continuum, infinity

• place, empty place

• solid body, object

• time, point of time

• (state) ?

Aristotle

Page 3: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Famous Space-Time Scientists

• Zenon of Elea 495 – 430

• Aristotle 384 – 322

• Galileo Galilei 1564 – 1642

• Isaac Newton 1643 – 1727

• Immanuel Kant 1724 – 1804

• Jules Henri Poincaré 1854 – 1912

• Max Planck 1858 – 1947

• Albert Einstein 1879 – 1955

• Werner Heisenberg 1901 – 1976

Page 4: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Recent Approaches in Temporal Logic

• Arthur Norman Prior: Tense Logic (1957)

P "It has at some time been the case that … ,

F "It will at some time be the case that … ,

H "It has always been the case that … ,

G "It will always be the case that ... .“

• Hans Kamp (Linguistics, Stuttgart University)

Spq "q has been true since a time when p was true"

Upq "q will be true until a time when p is true"

• Johan van Benthem (ILLC Amsterdam, CSLI Stanford)

The Logic of Time (1983)

Logic and the Flow of Information (1991)

Page 5: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Precision and Granularity

Aristotle

(Physics, book VI, 239a, 23):

During the time when a system is moving, not only moving in some of its parts,

it is impossible that the moving system is precisely at a certain place.

We need a theoretical treatment of granularity!

Page 6: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Einstein’s Granularity Remark

Albert Einstein:

„Zur Elektrodynamik bewegter Körper“

Annalen der Physik 17 (1905): 891-921

Footnote on page 893:

„Die Ungenauigkeit, welche in dem Begriff der Gleichzeitigkeit zweier Ereignisse an (annähernd) demselben Orte steckt und gleichfalls durch eine Abstraktion überbrückt werden muß, soll hier nicht erörtert werden.“

Page 7: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Partial Solutions in Modern Time Theories

• Automata Theory: States, Transitions

generalized by

• Labeled Transition Systems with Attributes:

No explicit time representation

• Petri Nets: States, Transitions, Token, Time

States and Transitions are

not related to Time

• Mathematical System Theory

What is a state? (Zadeh 1964)

What is a system? (Lin 1999)

Page 8: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

• Something which is stable for a moment?

• Stable: Constant as to some granularity

• Moment (instant, point of time): A time object described in some context

• For each moment the system should be in exactly one state!

What do we mean by a State of a System?

Page 9: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Conceptual Time Systems

Description of ...

• Temporal systems as scaled many-valued contexts

• Instants as formal objects (time granules)

• Granularity by Conceptual Scales

Then

• States are defined as object concepts

Page 10: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Example: Air Conditioning Plant

At any hour:

Temperatures:

OutdoorRoom 3Room 2Hot Water

In the following:Only for 3 days

Time Object Day Hour Outdoor-Temp Room3-Temp Room2-Temp Hot Water Temp100 1 0 3,3 19,6 19,7 32,6101 1 1 3,3 19,6 19,7 32,6102 1 2 3,3 19,5 19,7 32,6103 1 3 3,3 19,5 19,7 32,6104 1 4 3,3 19,5 19,7 32,6105 1 5 3,3 19,5 19,6 32,6106 1 6 3,3 19,5 19,8 33,8107 1 7 3,3 20,3 21,1 39,9108 1 8 3,3 21 21,4 40109 1 9 3,4 21,5 21,4 40110 1 10 3,3 21,8 21,5 40111 1 11 3,7 22,1 21,6 40112 1 12 4,1 22,4 21,6 40113 1 13 4,4 22,6 21,7 40114 1 14 4,2 22,8 21,7 40115 1 15 4,4 22,9 21,7 40116 1 16 4,7 22,9 21,7 40117 1 17 4,9 23 21,8 40118 1 18 5,3 23 21,8 40119 1 19 5,3 23,1 21,8 40120 1 20 5,4 23,1 21,8 39,2121 1 21 5,4 22,5 21,6 36,5122 1 22 5,1 21,9 21,2 34,8123 1 23 4,7 21,5 20,9 33,5

Page 11: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Temperatures during the first three days

0

5

10

15

20

25

30

35

40

45

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71

Outdoor Temperature

Room 3 Temperature

Room 2 Temperature

Hot Water Temperature

Page 12: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

What is a state of this system?

0

5

10

15

20

25

30

35

40

45

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71

Outdoor Temperature

Room 3 Temperature

Room 2 Temperature

Hot Water Temperature

The same state in three situations!

Page 13: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Situations: state-time pairsfor the outdoor temperatureand the hours (not the days)

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

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120121122321

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100101102103104105106107203<...>

108109110111208209210308309310

219

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300301302303304305306

221221223

Page 14: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

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120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 15: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 16: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 17: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 18: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 19: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 20: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

First Day

Page 21: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 22: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 23: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 24: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 25: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 26: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 27: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 28: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 29: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 30: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 31: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 32: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 33: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 34: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Second Day

Page 35: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

118119216316

120121122321

200201202206

211311

112113114115312313314315 116

117217218317318319

123320322323

100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Third Day

Page 36: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

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A movie in situation space:

Outdoor Temperature

Third Day

Page 37: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

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108109110111208209210308309310

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A movie in situation space:

Outdoor Temperature

Third Day

Page 38: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

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108109110111208209210308309310

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A movie in situation space:

Outdoor Temperature

Third Day

Page 39: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

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A movie in situation space:

Outdoor Temperature

Third Day

Page 40: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

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108109110111208209210308309310

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A movie in situation space:

Outdoor Temperature

Third Day

Page 41: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

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100101102103104105106107203<...>

108109110111208209210308309310

219

220

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221221223

A movie in situation space:

Outdoor Temperature

Third Day

Page 42: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

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Stunde: >=12

Stunde: >=16

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100101102103104105106107203<...>

108109110111208209210308309310

219

220

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221221223

A movie in situation space:

Outdoor Temperature

Third Day

Page 43: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

214215

213

212

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120121122321

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112113114115312313314315 116

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100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Third Day

Page 44: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

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100101102103104105106107203<...>

108109110111208209210308309310

219

220

300301302303304305306

221221223

A movie in situation space:

Outdoor Temperature

Third Day

Page 45: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Stundeo5iaus6

aussen: <=3.0

aussen: <=4.0

aussen: <=5.0

aussen: <=6.0

aussen: <=7.0

aussen: <=7.4Stunde: 0-23

Stunde: >=12

Stunde: >=16

Stunde: >=20

Stunde: >=8

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108109110111208209210308309310

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221221223

A movie in situation space:

Outdoor Temperature

Third Day

Page 46: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

What is a transition?

In Temporal Concept Logic:For the definition of states we do not need an ordering on the set G time objects.For introducing transitions we use a time relation R on G.A basic R-transition is defined as an element (g,h) of R.For f: G X the induced transition on X is defined as( (g,h), f(g), f(h) ).Example: Transitions in the state space or in the situation space.

Page 47: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Life tracks and objects

birth

copy

cooperation

One object at the same point of time

in two different situations??

Page 48: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Objects as subsystems

forbidden

Each object is in each moment g

in exactly one situation.

Page 49: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

The state space of a family (in the language of the therapeut)

Page 50: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

Transitions in Automata

In Automata Theory: A transition is a labeled pair of states.The order of time is represented only by the names„initial states“ and „terminal states“.

Automata and even the more general structure of Labeled Transitions Systems with Attributes (LTSA)can be represented by conceptual time systems (with actual objects and a time relation) such that the automaton-transitions are represented by conceptual transitions.(Map Reconstruction Theorem)

Page 51: Temporal Concept Logic Objects, States, and Systems Karl Erich Wolff University of Applied Sciences Darmstadt Ernst Schröder Center for Conceptual Knowledge.

The Map Reconstruction Theorem


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Wolff. Logic

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Erich Froom

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ALBUM OF ERICH SCHATZKI - · PDF fileALBUM OF ERICH SCHATZKI 1. 1898 – 1991 Erich Schatzki and Family Erich Schatzki, born January 23 1898, in Klafeld (Siegen) Nord-Rhein Westfalen,

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