experience based nonmonotonic reasoning · example wearewaitingforthetram,andit’sasunnyday... ......
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Experience Based Nonmonotonic Reasoning
Daniel Borchmann
TU Dresden
2013-09-16
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 1 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?
§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on time
But then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?
§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?
§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?
§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?
§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?
§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?§ No prior logical knowledge
§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
ExampleWe are waiting for the tram, and it’s a sunny day . . .
§ . . . so we expect our tram to be on timeBut then we hear some sirens (may a nearby accident?) . . .
§ . . . so our tram may be late
ObservationNon-monotonic behavior!
How to model?§ No prior logical knowledge§ Previous experiences
Decide what to expect based on previous experiences in similar situations
ApproachFormalize this situation using formal concept analysis (FCA)
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 2 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
Example
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ExampleOn what days was it sunny and the tram was on time?
t sunny, tram on time u1 = tDay 1,Day 3,Day 4,Day 6 u
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ExampleOn what days was it sunny and the tram was on time?
t sunny, tram on time u1
= tDay 1,Day 3,Day 4,Day 6 u
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ExampleOn what days was it sunny and the tram was on time?
t sunny, tram on time u1 = tDay 1,Day 3,Day 4,Day 6 u
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
Example
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ExampleWhat observations have Day 1 and Day 5 in common?
tDay 1,Day 5 u1 = t sunny u
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ExampleWhat observations have Day 1 and Day 5 in common?
tDay 1,Day 5 u1
= t sunny u
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ExampleWhat observations have Day 1 and Day 5 in common?
tDay 1,Day 5 u1 = t sunny u
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
IdeaIf it is sunny, it normally follows that the tram is on time if this has happenedoften enough in similar situations.
§ True for Day 1, Day 3, Day 4, Day 6§ Not true for Day 5
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
IdeaIf it is sunny, it normally follows that the tram is on time if this has happenedoften enough in similar situations.
§ True for Day 1, Day 3, Day 4, Day 6
§ Not true for Day 5
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
IdeaIf it is sunny, it normally follows that the tram is on time if this has happenedoften enough in similar situations.
§ True for Day 1, Day 3, Day 4, Day 6§ Not true for Day 5
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ObservationIf is sunny and there are sirens, it is not clear whether the tram will be on time
§ True on Day 4§ Not true on Day 5
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ObservationIf is sunny and there are sirens, it is not clear whether the tram will be on time
§ True on Day 4
§ Not true on Day 5
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ObservationIf is sunny and there are sirens, it is not clear whether the tram will be on time
§ True on Day 4§ Not true on Day 5
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
Example
sunny sirens tram on time
Day 1 ˆ ˆ
Day 2 ˆ
Day 3 ˆ ˆ
Day 4 ˆ ˆ ˆ
Day 5 ˆ ˆ
Day 6 ˆ ˆ
ObservationIf is sunny and there are sirens, it is not clear whether the tram will be on time
§ True on Day 4§ Not true on Day 5
Not enough evidence!
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 3 / 6
GoalFormalize notion of “normally follows”
ApproachUse notion of confidence: define for X ,Y sets of attributes
conf(X Ñ Y ) :=
#
1 X 1 = H|(XYY )1|
|X 1|otherwise
as the confidence of X Ñ Y .
Exampleconf(t sunny u Ñ t tram on time u) = 4/5
conf(t sunny, sirens u Ñ t tram on time u) = 1/2
ApproachConsider implications with high confidence as “normally true”
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 4 / 6
GoalFormalize notion of “normally follows”
ApproachUse notion of confidence:
define for X ,Y sets of attributes
conf(X Ñ Y ) :=
#
1 X 1 = H|(XYY )1|
|X 1|otherwise
as the confidence of X Ñ Y .
Exampleconf(t sunny u Ñ t tram on time u) = 4/5
conf(t sunny, sirens u Ñ t tram on time u) = 1/2
ApproachConsider implications with high confidence as “normally true”
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 4 / 6
GoalFormalize notion of “normally follows”
ApproachUse notion of confidence: define for X ,Y sets of attributes
conf(X Ñ Y ) :=
#
1 X 1 = H|(XYY )1|
|X 1|otherwise
as the confidence of X Ñ Y .
Exampleconf(t sunny u Ñ t tram on time u) = 4/5
conf(t sunny, sirens u Ñ t tram on time u) = 1/2
ApproachConsider implications with high confidence as “normally true”
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 4 / 6
GoalFormalize notion of “normally follows”
ApproachUse notion of confidence: define for X ,Y sets of attributes
conf(X Ñ Y ) :=
#
1 X 1 = H|(XYY )1|
|X 1|otherwise
as the confidence of X Ñ Y .
Exampleconf(t sunny u Ñ t tram on time u) = 4/5
conf(t sunny, sirens u Ñ t tram on time u) = 1/2
ApproachConsider implications with high confidence as “normally true”
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 4 / 6
GoalFormalize notion of “normally follows”
ApproachUse notion of confidence: define for X ,Y sets of attributes
conf(X Ñ Y ) :=
#
1 X 1 = H|(XYY )1|
|X 1|otherwise
as the confidence of X Ñ Y .
Exampleconf(t sunny u Ñ t tram on time u) = 4/5
conf(t sunny, sirens u Ñ t tram on time u) = 1/2
ApproachConsider implications with high confidence as “normally true”
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 4 / 6
GoalFormalize notion of “normally follows”
ApproachUse notion of confidence: define for X ,Y sets of attributes
conf(X Ñ Y ) :=
#
1 X 1 = H|(XYY )1|
|X 1|otherwise
as the confidence of X Ñ Y .
Exampleconf(t sunny u Ñ t tram on time u) = 4/5
conf(t sunny, sirens u Ñ t tram on time u) = 1/2
ApproachConsider implications with high confidence as “normally true”
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 4 / 6
So what?
§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!
§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new
§ Should exist similar approaches, much better investigated
Still interesting!
§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!
§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!
§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!§ Shows connection between FCA and NMR
§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining
§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data
§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
So what?§ Approach does not seem to be new§ Should exist similar approaches, much better investigated
Still interesting!§ Shows connection between FCA and NMR§ FCA provides interfaces to Data Mining§ Approach may be used to mine “non-monotonic rules” from data§ Closer look on connections between this approach and existing ones
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 5 / 6
Thank You
Daniel Borchmann Experience Based Nonmonotonic Reasoning 2013-09-16 6 / 6
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